Two-time World Matchplay winner van Gerwen defeated Cullen in a repeat of last month’s Cazoo Premier League final, after Wright denied Ratajski in the game of the tournament so far.
The world champion had looked poised to breeze through to the last eight after storming into a 7-3 lead.
Ratajski rallied, reeling off four consecutive legs to draw level, before defying a magnificent 10-darter from Wright by landing back-to-back 180s in a 12-dart riposte.
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Nevertheless, the Polish number one was staring down the barrel after squandering three darts to break throw and lead 10-9, with Wright leaving 16 after nine darts in the following leg.
However, the world number one returned the favour by frittering away three match darts and Ratajski capitalised, sinking a two-dart 77 combination to send the contest into overtime.
It was Wright who kept his cool, following up a third 11-darter by pinning double 10 to triumph and set up a repeat of last year’s final against Dimitri Van den Bergh in the last eight.
Van den Bergh recovered from a sluggish start to complete an 11-6 victory over Rowby-John Rodriguez in Tuesday’s opener.
The 2020 champion, bidding to reach a third consecutive World Matchplay final, reeled off four straight legs to establish a 4-2 cushion.
Rodriguez spurned one dart at double 16 to level at 5-5 and was suitably punished by the Belgian, who extended his lead to 8-4.
The Austrian reduced the arrears with a fifth maximum and a 13-darter, but this only provided a temporary reprieve as Van den Bergh wrapped up a convincing victory with a stunning 146 outshot.
Van Gerwen’s hopes of a World Matchplay hat-trick are still alive after he eased past a profligate Cullen.
The Dutchman was below-par in his opening round win over Adrian Lewis, yet showed no signs of fragility in the early exchanges against Cullen to open up a 4-1 lead.
The high scoring continued in leg six, as Cullen cut the deficit with a 12-dart break to double his tally.
However, the Masters champion never recovered from squandering four darts at double to level proceedings, with van Gerwen winning seven of the final nine legs to complete a comprehensive 11-5 success.
Van Gerwen will take on Nathan Aspinall in the last eight after he edged out 2007 champion James Wade, 11-9.
Wade landed three ton-plus checkouts within the opening 10 legs to level at 5-5 before winning back-to-back legs to move 7-5 up.
Aspinall responded emphatically, following up a 13-darter with a 68 finish before landing a crucial 82 checkout on tops in leg 17 to secure the lead, which he cemented with a comfortable hold of throw.
Wade preserved his hopes with a 13-darter but Aspinall stormed to victory by following up a third maximum with an 81 combination for a 12-dart hold.
The second round draws to a close tonight as Gerwyn Price meets Dave Chisnall, Michael Smith plays Dirk van Duijvenbode, Rob Cross takes on Jose De Sousa and Danny Noppert faces Daryl Gurney.