With reigning champion Phil Taylor, two-time winner James Wade and Raymond van Barneveld already knocked out of the event, double world champion Lewis followed after a sloppy performance against the Dutchman.
Van Gerwen came flying out of the traps and swept to the first set, and although Lewis replied in kind with the second the Dutchman hit back in a more even third to go back in front.
A superb 170 finish from Lewis kicked-off the fourth set, but Van Gerwen managed to get back into it with sloppy visits from the world champion seeing him regularly fall behind in the scoring.
The Dutchman was left with a simple two-dart kill at 44 to seal his passage into the quarter-finals after taking out a huge scalp in Lewis as the big names continued to stumble in Dublin.
"I'm very happy to win in a tournament like this against the world champion, it means a lot to me," Van Gerwen told Sky Sports. "This is a big step for me with another good result in another major tournament.
"I've taken some confidence from recent games and I'm glad I could take it into that match - I had some loose darts out there but I kept in there fighting and hopefully my game can improve from here."
Andy Hamilton is up next for van Gerwen after he came through a ding-dong tussle with Steve Beaton - coming from 2-1 down to win the next two sets and prevail 3-2.
In an even contest it just came down to the finishing doubles, with Hamilton hitting over half his attempts as he stays in with a shout of winning his first major title.
"I've made every major quarter-final apart from the UK Open this year, so I'm showing that I deserve to be in the top eight - there's no reason why I can't win this now," said The Hammer.
"Once Phil Taylor goes out of the tournament, even though he was in the opposite half to me, everybody pushes up their game because he's such a great player. There's going to be a new name on the trophy, and hopefully it's mine."
Paul Nicholson beat Colin Osborne 3-1 to also make the last eight.
'The Asset' has been struggling of late and was in danger of sliding out of the world's top 16 heading to Dublin, but he looked more like his old self in a typically battling performance against Osborne.
Nicholson will now go up against one of only two seeds to be left standing in the last eight in Wes Newton after he managed to grind out a 3-1 win over Ian White.
Newton edged a nervy first set, but White started to assume control in the second and after taking that went on to dominate the third and looked odds-on to go in front.
However, he missed three darts for the set at double 18 and Newton took out 88 before following up in the next and winning a set that he never looked like having a chance in.
That proved to be just the catalyst Newton needed and he produced his best darts of a scrappy match in the next set to take it and go through 3-1 to set up a meeting with Nicholson.