Selby struggled for form throughout and despite winning the opening frame it was no surprise to see him 3-1 down at the interval.
He had his fair share of bad luck, but his potting was not at its best as he made a number of mistakes.
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Rising star Zhou was more than happy to capitalise and he looked in a good position at 5-3.
However, Selby dug deep and battled back to level with breaks of 65 and 79, his first half-century runs of the match.
He then dominated the final frame to set up a third round clash with either Ding Junhui or Mark Allen.
Elsewhere, Barry Hawkins comfortably beat Stephen Maguire 6-3.
Hawkins knocked in runs of 114, 103, 99 and 91 on his way to victory despite a century for Maguire in frame four.
He will now face the winner of the match between Anthony McGill and world champion Mark Williams.
Earlier on Tuesday, McGill beat Yan Bingtao 6-2 in the first match of the day to make it through to the second round.
McGill, who made the last four of the English Open last year, started in imperious form with breaks of 69, 134 and 67 to race into a 3-0 lead.
Bingtao closed the gap to 3-2, including a big break of 133 but that was as good as it got for the 18th seed.
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McGill kicked up a gear and knocked in consecutive breaks of 79 and 62 to wrap up victory.
In the first round's other early match, Ryan Day, a two-time ranking event winner last season, saw off amateur Chang Bingyu 6-2.
Chang didn't make a single break over 50 whilst Day scored knocks of 90, 73, 130 and 100 on his way to victory.
The Welshman will face John Higgins on Wednesday.

Shanghai Masters Round Two Results

Mark Selby 6-5 Zhou Yuelong
Barry Hawkins 6-3 Stephen Maguire

Shanghai Masters Round One Results

Anthony McGill 6-2 Yan Bingtao
Ryan Day 6-2 Chang Bingyu