The Dutchman averaged 108.5, landed a 13-dart hold to start, broke early when Anderson missed at double 4, then crucially punished a missed bull for 170 with double 14 for 4-1 before closing on double 8.
The result sets up a knockout meeting with Danny Noppert.
"Gary is a player with huge talent and calibre," MVG told Sky Sports after the victory.
"He's a fantastic player, but I'm glad I won today.
"But if you look at the perspective of myself and him, I'm the better player.
"Of course, I can say whatever I want now - but you have to show it on stage."
Defending champion Luke Littler completed a perfect Group E with a 5-1 win over Daryl Gurney.
Littler opened with back-to-back 180s, repeatedly left his preferred double 10 and twice laid up attempts at the big fish after purposeful set-ups, delivering the statement he had promised before the session.
Connor Scutt joined him in the knockouts as group runner-up after a 5-3 victory against Karel Sedlacek, built on the night's key break on 68 and a composed tops to finish after a brief stumble on 51.
Beau Greaves closed her group campaign with a 5-3 comeback over Niko Springer in Group G.
Trailing 0-3, she reeled off five straight legs, including a 134 on double 7, and produced back-to-back 180s to tee up the finish.
It was not enough to progress, though it underlined the quality of her performances across the section.
Jonny Clayton bowed out with a win, edging Noppert 5-4 in Group H.
Already eliminated, Clayton forced the decider with a 120 finished on tops and then tidied 50 to take the match, a neat reminder of his end-game reliability even in a lean year.
Elsewhere, Lukas Wenig defeated Cam Crabtree 5-1 to top Group H, highlighted by a 167 on the bull that turned the match.
Wessel Nijman whitewashed Lisa Ashton 5-0 to advance from Group F, and Josh Rock beat Gian van Veen 5-2 to claim the other spot, sealing it with a 13-darter on double 18 after capitalising on missed doubles.
Tuesday's results:
Jonny Clayton 5-4 Danny Noppert
Niko Springer 3-5 Beau Greaves
Luke Littler 5-1 Daryl Gurney
Lukas Wenig 5-1 Cam Crabtree
Connor Scutt 5-3 Karel Sedlacek
Michael van Gerwen 5-2 Gary Anderson
Wessel Nijman 5-0 Lisa Ashton
Gian van Veen 2-5 Josh Rock