Huybrechts had suffered six consecutive first round exits on the famous Blackpool stage but broke his duck against Henderson to kick off night three in Blackpool with a bang.
The Belgian had to survive a match dart in a dramatic deciding leg before finding double eight to claim victory in a high class contest which saw 13 180s and five ton-plus finishes.
"I am so relieved to finally win a game on this stage," said Huybrechts, who will face Peter Wright in round two.
"I was certain that John was going to hit double top and win the match but when he didn't I knew I had to take my chance and thankfully I did.
"It's never easy playing under such huge pressure but I'm so happy to win and now I'm going to enjoy this moment."
The former Premier League star raced into a 5-1 lead before Henderson battled back to 6-6 and then took out 60 to take the lead for the first time in the tie at 9-8.
Huybrechts broke straight back with an 85 finish to save the match and take the game to a first tie-break of the evening.
The Belgian missed four match darts in the tie-break, as Henderson took the match all the way to 12-12.
With Huybrechts unable to watch, Henderson missed a match dart of his own at double 20 before the Belgian stepped up to take out 32 and seal his passage into round two for the first time.
Last year's beaten finalist Wright cruised to a 10-5 victory over Jelle Klaasen in the final game of the first round, hitting a roof-raising 170 finish along the way.
The former UK Open champion struck a 122 checkout to move 3-0 up and found himself in a commanding 4-1 lead heading into the first break.
Klaasen fought his way back to 9-5 but was unable to get close to challenging for the lead as Wright marched onto the last 16 for a fourth successive year.
"I wanted to play a lot better than I did tonight," said Wright, the 9/2 second favourite with sponsors BetVictor.
"Ideally I would've produced a ton-plus average but there's a long way to go in the tournament and I'm confident I will beat Kim in the next round."
The only former champion remaining in the tournament, James Wade, was made to work hard for a 12-10 win over Jermaine Wattimena in the second tie-break of the evening.
With neither player producing their best game, the six-time Winter Gardens finalist was unable to shake off a stubborn Wattimena, who fought back from 9-7 to take the game into additional legs.
Wade held throw to take an 11-10 lead before landing double 18 to find the match-winning break of throw and set up a round two clash with Simon Whitlock.
"That was a very frustrating game for me, I thought I was going to play a lot better than that," Wade admitted.
"I just wanted to go up there and play well and not get involved in a scrap because it's never nice.
"I was nervous and anxious to get over the finishing line which, thankfully, I did in the end but I will need to play a lot better than that."
Whitlock secured a convincing 10-2 victory over his close friend and Winter Gardens debutant Richard North.
The Australian flew into a 4-0 lead and, with 36 points separating North from registering his first leg, Whitlock hit a crucial 126 finish to go into the break with a commanding five leg cushion.
The two-time Blackpool semi-finalist made it 8-0 before North won back-to-back legs to make it 8-2, but they proved to be nothing more than a consolation as Whitlock progressed to round two for the sixth time in eight years.
"Richard is a fantastic dart player, a lot better than he showed tonight," said Whitlock.
"It's never easy playing a friend but I felt relaxed during the match and I'm happy to make it through."
The £500,000 tournament continues on Tuesday at Blackpool's Winter Gardens, with four second round ties including Gary Anderson taking on Raymond van Barneveld.
Jeffrey de Zwaan, who knocked out world number one Michael van Gerwen, plays 2013 finalist Adrian Lewis, Michael Smith meets St Helens rival Dave Chisnall and Daryl Gurney takes on Joe Cullen.
Following the opening three days of action, Anderson is outright favourite to win the World Matchplay title at 11/4 with sponsors BetVictor, with Cross at 7/2.
2018 BetVictor World Matchplay
Schedule of Play
Monday July 23
Kim Huybrechts 13-12 John Henderson
Simon Whitlock 10-2 Richard North
James Wade 12-10 Jermaine Wattimena
Peter Wright 10-5 Jelle Klaasen
Tuesday July 24 (7pm)
Dave Chisnall v Michael Smith
Daryl Gurney v Joe Cullen
Jeffrey de Zwaan v Adrian Lewis
Gary Anderson v Raymond van Barneveld
Wednesday July 25 (7pm)
Simon Whitlock v James Wade
Mensur Suljovic v Ian White
Rob Cross v Darren Webster
Peter Wright v Kim Huybrechts
Best of 21 legs
* Each game must be won by two clear legs, with up to a maximum of five additional legs being played before the sixth additional leg is sudden-death. For example, should a Second Round game (best of 21 legs) reach 13-13, then the 27th leg would be the final and deciding leg.
BetVictor Outright Winner Odds - Following Round One
11/4 Gary Anderson
7/2 Rob Cross
9/2 Peter Wright
8/1 Michael Smith
10/1 Mensur Suljovic, Adrian Lewis, James Wade
16/1 Daryl Gurney
18/1 Raymond van Barneveld
33/1 Joe Cullen, Ian White, Simon Whitlock
40/1 Dave Chisnall
66/1 Jeffrey de Zwaan, Darren Webster, Kim Huybrechts
Written by Josh Phillips