Reigning champion van Gerwen was in dominant mood as he defeated 2013 Grand Slam finalist Thornton 10-5 as the last 16 kicked off at the Wolverhampton Civic Hall.
The world number one's opening 11-darter was followed by a 129 finish from Thornton as the Scot shared the first four legs, but van Gerwen pulled clear with four in a row to move 6-2 up.
Thornton hit back with a brilliant 145 checkout, but van Gerwen bettered that with the maximum 170 finish on his way into a 9-4 lead before landing another 11-darter to secure the victory.
"I felt comfortable and I played okay in patches, but Robert is a fighter and you know you have to take an extra step against him," said van Gerwen.
"I'm in great form and the next game is Brendan Dolan - he's a good player who I played in the group and I hope I can beat him again. That's the next target in this tournament."
Northern Irish ace Dolan won through to Friday's quarter-finals by producing a memorable comeback to edge out Gerwyn Price in a deciding leg as he moved into the quarter-finals for the first time in Wolverhampton.
Price raced into a 4-0 lead and also led 5-1 before Dolan hit back to level, and the former World Grand Prix finalist then followed up a 160 checkout with a brilliant 157 finish as he moved ahead for the first time at 8-7.
Price levelled and shared the next two to force a decider, but Dolan opened the final leg with his seventh 180 before finishing 101 to complete the fightback.
"I'm so relieved," said Dolan. "I had to dig really deep there to try and get the result and I'm delighted to get through.
"At the start it wasn't looking good for me and I was snatching my darts, so to get back to five-all was a bonus. I knew I still had a job to do because Gerwyn's a fighter, but I stuck with him and kept the pressure on with some big finishes."
Six-time Grand Slam winner Taylor continued his bid to complete another Wolverhampton triumph with a 10-5 win over Canada's Jeff Smith, the BDO Lakeside Championship finalist who had won through to the last 16 in his debut in the event.
However, despite sharing the opening four legs, Smith was punished for missed doubles as Taylor took five legs in a row - including a neat 100 finish with two double tops - to move 7-2 up.
Smith took out a memorable 152 checkout as he hit back, but the Canadian was unable to prevent Taylor from securing his place in the quarter-finals on Friday.
"I'm pleased to be through but not pleased with my performance," said Taylor, who averaged 98 and finished 42 percent of his chances at a double. "That performance isn't good enough and I've got to improve for the quarter-finals.
"I felt good tonight but I'll get back on the practice board on Thursday now and make sure I'm right for the quarter-finals."
Taylor now meets number five seed Peter Wright, who claimed eight successive legs as he overcame Darryl Fitton 10-3 to reach the quarter-finals in Wolverhampton for the first time.
A pair of 14-dart finishes gave Wright an early edge before BDO World Trophy champion Fitton finished 76 and 48 to move himself 3-2 up.
Wright, though, ignited his challenge by following a 13-darter with a 106 finish as he pulled clear, before completing victory with a 99 checkout - and although he progressed to the last eight was unimpressed with his performance.
"I still know there's more in the tank," said Wright. "I thought I was terrible but I set myself high standards and I didn't meet them tonight.
"I'm not just happy with going through, I want to do to people what Phil Taylor did years ago, and that's why I'm coming off annoyed. I have some great battles with Phil and it should be another one on Friday."
The second round concludes on Thursday night with the remaining four matches, including 2012 champion Raymond van Barneveld taking on BDO number one Glen Durrant.
2010 Grand Slam of Darts runner-up James Wade meets Benito van de Pas, PDC World Champion Gary Anderson plays Dutchman Danny Noppert and local ace Jamie Hughes meets youngster Chris Dobey.
Tickets for the SINGHA Beer Grand Slam of Darts can be purchased by calling 0870 320 7000 or online at www.theticketfactory.com/PDC.
SINGHA Beer Grand Slam of Darts
Wednesday November 16
Gerwyn Price 9-10 Brendan Dolan
Phil Taylor 10-5 Jeff Smith
Michael van Gerwen 10-5 Robert Thornton
Peter Wright 10-3 Darryl Fitton
Thursday November 17 (7pm)
4x Second Round
Jamie Hughes v Chris Dobey
Benito van de Pas v James Wade
Gary Anderson v Danny Noppert
Raymond van Barneveld v Glen Durrant
All games are the best of 19 legs