Bingham, who knocked six-time champion Steve Davis out in the first round, resumed with a 5-3 advantage - only for Perry to win three frames in a row to lead for the first time in the match.
It was a largely scrappy affair, Perry's break of 55 in the 10th frame the highlight, and Bingham was grateful to claim the 12th frame to go into the mid-session interval level at 6-6.
On the other table, China's Liang Wenbo, conqueror of Ken Doherty in the first round, led Northern Ireland's Joe Swail 7-4.
Liang led 6-2 overnight but Swail took two of the first three frames of the day to reduce his deficit slightly.
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