An out-of-sorts Perry then fluffed his lines when potting a red to the middle pocket with a relentless Milkins making no mistake to move to one behind, and then drawing level to set up a three-frame shootout.
Milkins clinched the next frame to put him on the brink of glory before Perry scrambled to produce a clearance of 63 and take the match to a decider.
But it was Milkins who held his nerve to secure the final frame and seal a memorable fightback. He will face Shaun Murphy or Si Jiahui in the next round.
Mark Selby saw off a determined challenge from qualifier Matthew Selt as the four-time champion started his bid for a fifth crown with a hard-fought 10-8 victory.
Selby led 6-3 overnight before moving 8-4 ahead on Thursday afternoon but Selt refused to shrink away in a battle that became increasingly attritional to narrow the deficit to 9-8.
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But Selby, winner of this event in 2014, 2016, 2017 and 2021, reeled off a 112 break to close out the win and set up a clash with Gary Wilson in the next round.
Elsewhere, three-time champion Mark Williams and qualifier Luca Brecel were all square at 4-4 after the first session of their second-round encounter.
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