The Dutchman looked to be heading through with the minimum of fuss when he took the first two sets and then the opening two legs of the third, only for Lewis to hit back and reduce the deficit with a 10-darter in the decider.
However, the respite was temporary as Van Gerwen, who averaged 108.08, produced back-to-back 11-dart finishes to take the fourth set 3-2 from 2-1 down and then complete a 4-1 victory by the same score in the fifth.
He told Sky Sports: "I made myself work hard, to be fair. I had a few darts to already be 3-0 up in sets and I gave him too much confidence. I shouldn't put myself in that position.
"But I think everyone could see my form is there. When I had to, I produced 11, 11, 11, 12 in the last two sets.
"From here, I can build on to the next round. I feel good."
World number four Gary Anderson survived a major scare to make it to the last eight with a thrilling 4-3 win over Chris Dobey.
Dobey, who hit a record-equalling 15 maximums in the match, led 2-0 and 3-2, but Anderson held his nerve and despite missing with five match darts, closed it out at 4-2 in the final set to progress.
Earlier, Dutchman Benito Van De Pas had completed the field for the last 16 with an edgy 4-2 victory over Toni Alcinas.
Van De Pas, who will face Brendan Dolan in the next round, checked out on 160, 149 and 151 on his way to victory, but was made to work hard for his win after surrendering a two-set lead.
In the afternoon session, World number 10 Michael Smith produced a concerted fightback to see off the challenge of Scotland's John Henderson.
Henderson landed a 161 check-out on his way to a 2-1 lead after three sets, but Smith rattled through the fourth in just 38 darts to level and then won six of the next seven legs to complete a 4-2 victory and set up a clash with Ryan Searle.
Luke Humphries will meet reigning champion Rob Cross after following up his second round victory over Steve Bunting with a 4-1 win over world youth champion Dimitri Van Den Bergh.
Humphries won the first two sets on last leg deciders and although Van Den Bergh hit back in the third, his opponent surrendered just one more leg as he eased over the finishing line.
African qualifier Devon Petersen made Steve West pay for missed doubles as he secured his 2019 PDC Tour Card as well as a place in the last 16 with a 4-2 victory.
Having lost the first set 3-0, Petersen hit finishes of 139 and 120 to take a 2-1 lead and although West levelled, he missed double top for a 3-2 lead and saw his opponent take full advantage.
There was further drama in the sixth set when West squandered the chance to save the match with five darts at tops to let the South African, who will now face Nathan Aspinall.