The Welsh world number 13 made a run of 131 to level the match at 1-1 after Perry opened up with a break of 75.
But he then lost three consecutive frames to the Fen Potter to trail 4-1 with the Englishman rattling home a 103 run in the process.
Stevens reduced the deficit with a break of 89 in frame six but it was Perry who moved into the last 16.
But there were no such problems for Stevens' fellow Welshman and world number three Mark Williams who defeated Mark Davis 5-1.
Williams, who lost the deciding frame in last year's final to Mark Selby, accounted for the Englishman who has reached the semi-finals of the first two ranking events of the year.
The two-time world champion Williams lost the opening frame but then reeled off five in a row featuring breaks of 53, 67 and 88.
Chinese teenager Lu Haotian produced the only shock in the six wild card matches as he won the deciding frame against Marco Fu to reach the last 32.
The 14-year-old, currently the IBSF World Under-21 champion, trailed 3-0 but had a break of 112 en-route to winning four frames in a row.
Hong Kong's Fu levelled with a 124 but Lu won the decider. He was on a 147 after potting the first 10 reds and nine blacks but missed the 11th red. However his 76 means he will go on to face World Open champion Mark Allen in the first round.
Six-time world champion Steve Davis had top breaks of 77 and 69 as he cruised through his clash against Zhu Yinghui 5-1 to set up a meeting with Ricky Walden and Robert Milkins edged through with a break of 61 in a deciding frame with Zhou Yuelong.
Ryan Day, Jamie Jones and Mark King beat Wang Yuchen, Lu Ning and Zhao Xintong 5-0, 5-2 and 5-3 respectively.