World Champion Anderson was denied the chance to face Adrian Lewis on medical grounds after being laid low with a viral upper respiratory tract infection on Thursday.
His absence meant that debutant Michael Smith played twice on the evening - and the former World Youth Champion was given a tough induction to the Premier League stage with losses to Peter Wright and Adrian Lewis.
However, the night's most eye-catching display came from Chisnall as he followed up a run to the final of last weekend's Masters event by storming past Thornton 7-0.
He allowed his rival only one dart at a double during a ruthless performance as he averaged over 101 to kick off the season in style.
"It's a dream," said Chisnall, a semi-finalist last year. "Robert didn't play as well as he can but I capitalised on his mistakes and hit my doubles well.
"It's going to get harder because it's only our second tournament back since the World Championship so everyone's rusty and there's more to come. Today was good for me."
2014 champion Raymond van Barneveld also produced a brilliant display of finishing as he took out seven doubles from nine attempts as he swept past six-time Premier League winner Phil Taylor 7-2.
Van Barneveld landed an early ten-darter as he came from a leg down to lead 5-1, and though Taylor took out 113 to hit back, the Dutchman went on to complete the win with a pair of double 16 checkouts.
"I'm happy with the win," said van Barneveld. "To get two points in the opening match of the Premier League against Phil Taylor, with a 103 average, I'm over the moon.
"The ten-darter gave me a lift and I hit lots of crucial doubles. I tried to keep Phil under pressure and maybe he wasn't at his best, but I took advantage of that.
"I'm focused on the Premier League because the Premier League and the World Championship mean the world to me. I focus on every match and I know what I can do - I believe in myself and I hope I can go all the way."
2009 Premier League winner James Wade impressed with a superb comeback from 3-0 down to defeat Michael van Gerwen 7-4, with the Dutchman hitting a 167 checkout as he took an early lead only to be punished for missed doubles in four of the next five legs.
A 70 finish from van Gerwen saw him pull back to 5-4, but Wade hit a 121 finish to restore breathing space before following his fifth 180 by finishing 81 on the bull for victory.
"I'm really happy because there are not many people who will take a point from Michael, because he's the best player in the world," said Wade. "Michael wasn't at his best and I did enough and hit my finishes when I had to.
"I can win games from bad situations and that's what I did."
Two-time World Champion Lewis - who had initially been due to face Anderson - topped a 100 average as he defeated Smith 7-1, reeling off six straight legs on his way to victory with seven doubles from 13 attempts.
"I thought my finishing tonight was fantastic," said Lewis. "Michael Smith's no mug, he's number eight in the world and he'll be back. It's his first time and it is hard because you're against the world's top ten week-in and week-out.
"My mind was set for playing Gary so I had to change my focus but I did that well. I love Leeds and I played brilliantly here last year, and the crowd were superb tonight."
World number five Wright opened the season with a 7-2 win over Smith, taking out 121 on his way into a 3-0 lead to establish a cushion which - despite two 14-darters from his opponent - he would never let slip.
"I've been working really hard in the last few weeks since the World Championship and it's great to be back playing," said Wright.
"It was a bit of a patchy display in places but it's a win and that was the most important thing, because every two points could prove crucial."
The Betway Premier League continues at the Metro Radio Arena in Newcastle next Thursday, with tickets still available by calling 0844 493 6666 or online via www.eventim.co.uk.
2016 Betway Premier League
Night One, First Direct Arena, Leeds
Peter Wright 7-2 Michael Smith
Michael van Gerwen 4-7 James Wade
Phil Taylor 2-7 Raymond van Barneveld
Robert Thornton 0-7 Dave Chisnall
Adrian Lewis 7-1 Michael Smith
Peter Wright v Michael Smith
1-0 - Wright takes the season's opening leg on double 16.
2-0 - Wright secures an immediate break of throw by taking out 121 on the bullseye.
3-0 - Wright lands a 180 to have the breathing space to miss five doubles, with Smith unable to capitalise on double eight as his rival returns to claim his third leg.
3-1 - The pair trade 180s before Smith steps in to punish Wright's miss at tops by taking out 84 for a 14-darter.
4-1 - Wright hits a 180 and tops for a 14-darter in reply.
5-1 - Another 180 sees Wright pull clear before double six gives him a fifth leg, after Smith misses tops.
5-2 - Smith finishes a second 14-dart leg of the match by landing double ten.
6-2 - Wright fires in a fifth 180 before double 16 completes a 12-dart finish.
7-2 - Another double 16 checkout for Wright seals a fine opening win.
Michael van Gerwen v James Wade
1-0 - Wade first in the game's first 180, but van Gerwen holds throw on double one to claim the opener.
2-0 - Wade lands another maximum, but can only watch on as van Gerwen finishes a stunning 167 checkout.
3-0 - van Gerwen opens with a 180 and adds a 177 before hitting tops to claim a third leg.
3-1 - A miss at tops from van Gerwen allows Wade in to hit double ten for his first leg.
3-2 - Double 12 sees Wade break throw.
3-3 - van Gerwen misses two darts at double 16, and Wade takes out a clinical 116 on double 18 to level.
3-4 - Wade lands a third 180 before hitting double ten to move ahead.
3-5 - van Gerwen hits a maximum of his own but pays for two further missed doubles as Wade steps in on tops for a fifth successive leg.
4-5 - The world number one finishes 70 on double 16 to reply with his first leg in six.
4-6 - Wade opens with a 180 before finishing 121 on double 14 to seal at least a point.
4-7 - The pair trade 180s before van Gerwen's miss at the bull allows Wade in, and he finishes 81 on the bull for victory.
Phil Taylor v Raymond van Barneveld
1-0 - Double eight gives Taylor the opening leg.
1-1 - van Barneveld hits a 180 and double 12 to level.
1-2 - van Barneveld opens with 140 and 180 before finishing double 18 for a ten-dart leg.
1-3 - Double 18 once more continues van Barneveld's flawless doubling.
1-4 - The Dutchman wins his fourth straight leg, breaking with a 61 finish on double 18.
1-5 - van Barneveld takes out 66 to hit a fifth double from as many attempts.
2-5 - Taylor takes out 113 to hit back.
2-6 - Taylor lands a 180, but sees van Barneveld take out 64 on double 16 to land another first-dart double and seal at least a point.
2-7 - van Barneveld misses two darts at double 16 to see his flawless finishing record ended, but Taylor's two misses at tops allow him back in to hit double 16 at the third time of asking to seal an opening win.
Robert Thornton v Dave Chisnall
0-1 - Chisnall capitalises on a slow start from Thornton - who kicks off with a score of 11 - by hitting double 16 to break immediately.
0-2 - Chisnall lands a 180 before finishing 54 for a 12-darter.
0-3 - Double eight sees Chisnall claim a third straight leg.
0-4 - Double eight for a 14-darter sees Chisnall continue his charge.
0-5 - Chisnall finishes 100 with two clinical darts to win a fifth leg, without Thornton yet having a dart at a double.
0-6 - Chisnall takes out 73 on double eight for a 14-darter to seal at least a draw.
0-7 - Thornton misses tops for a 117 finish - his first chance at a double - to allow Chisnall in to complete a 13-darter for only the sixth Premier League whitewash.
Adrian Lewis v Michael Smith
1-0 - Lewis lands an early 180 before finishing 72 on double four to take the opening leg.
1-1 - Two misses at tops from Lewis allow Smith in to hit the same bed and level.
2-1 - Smith misses three darts to break throw, allowing Lewis back in on double ten.
3-1 - Lewis breaks throw by finishing 76 on double eight to move two legs clear.
4-1 - Lewis lands a 177 as he takes out a 14-darter to win a third successive leg.
5-1 - Tops sees Lewis break throw once more to pull clear.
6-1 - Lewis kicks off with a 180 before finishing 84 for an 11-dart leg.
7-1 - The Stoke ace lands his third maximum before finishing 84 once again as a 12-darter seals a big win.