Higgins, the world number four, was widely expected to make light work of his much lower-ranked rival but found himself in early trouble as Wen took the first two frames with breaks of 53 and 92.
A scrappy third frame went the way of Higgins but Wen headed to the mid-session interval with a 3-1 lead when edging a tight fourth frame.
Higgins finally found some rhythm in the next, a run of 73 reducing his arrears to 3-2, but a break of 56 put Wen within touching distance of victory at 4-2.
Wen couldn't get over the line, though, and Higgins drew level with a well-taken break of 85 before dominating a deciding frame that went scrappy when the bulk of the reds found themselves clustered around the top side-cushions.
Higgins will play Scott Donaldson in round three after the latter got the better of Jack Lisowski.
World champion Mark Williams is through after overcoming Gary Wilson 5-2 while world number one Mark Selby was a 5-1 winner over Chinese wild card Chang Bingyu.
A repeat of the 2010 World Championship final saw Graeme Dott beat Neil Robertson 5-2 while Judd Trump saw off Jamie Jones 5-2 and Shaun Murphy beat Xiao Guodong by the same score.
Yan Bingtao was also a 5-2 winner over Stuart Bingham and Iran's Hossein Vafaei is through after a 5-3 win over Ryan Day.
Ding Junhui suffered a shock defeat to teenager Yuan Sijun.
Yuan, 18, who turned professional last year, took a dramatic deciding frame to seal a 5-4 victory and reach the last 16 of a ranking event for the first time.
He will now play Mark King, who was a comfortable 5-1 winner against Masters champion Mark Allen.