World number one Van Gerwen averaged 112 to win the opening set without reply and raced into a 2-0 lead before a brilliant 170 finish secured him the third.
Hopp stopped the rot by taking the fourth set as Van Gerwen eased off the gas and moved 2-0 ahead in the fifth.
But the German missed a huge checkout and Van Gerwen landed a double 19 to break his opponent before going on to take the last three legs.
Two-time champion Van Gerwen, who finished with a 101.51 average, will play either Adrian Lewis or Darius Labanauskas in the fourth round.
Gary Anderson survived a match dart and won a thrilling tie-break to squeeze through 4-3 against Dutchman Jermaine Wattimena in the evening’s penultimate match.
Leading 2-0 in the deciding set, Wattimena missed the bull for a 170 checkout to win it and two-time champion Anderson forced the tie-break.
Wattimena then produced a 104 checkout to lead the tie-break 3-2, but an 80 finish from Anderson levelled it up at 3-3 and the Scot held his nerve to seal a memorable win. He will play Vincent van der Voort or Chris Dobey in the last 16.
Should they win their respective quarter-finals, Van Gerwen and Anderson ae due to meet in the last four for a place in the final.
Ryan Searle hit back from a set down in the first match of the evening session to cruise through to the last 16 with a 4-1 win against Irishman William O’Connor.
Lewis went all the way to the semi-finals last year, despite being a qualifier, but has enjoyed limited success since.
Gurney has become one of the sport’s leading names in that time and few thought the Northern Irishman would follow the likes of Peter Wright, Mensur Suljovic and Gerwyn Price in going home before Christmas.
But that was how it turned out in their third-round clash, Lewis winning 4-3, having led 2-0 and 3-1, with Gurney throwing for the match and failing to close it out.
Earlier, another seed, the 25th-ranked Alan Norris was knocked out by Ryan Joyce, a man travelling a path similar to Lewis a year ago.
Joyce beat Simon Whitlock in the last round and came from 2-0 down to beat Norris 4-3.
There was no such drama for Dave Chisnall, though, a 4-0 winner over Kim Huybrechts.
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