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Reece Styche came close for Wycombe early on when he turned his man and fired an effort at the post.
The hosts were again denied by the woodwork minutes later when Max Kretzschmar's drive came back off the frame of the Rochdale goal.
Kretzschmar then saw his free kick go wide for the hosts just before the break.
After the restart, Allen volleyed in to put the visitors in front following good play from Sam Wood.
They then doubled their advantage when Vincenti turned home after a scramble from a corner.
Ingram had saved from Olly Lancashire in the first instance, but the ball wasn't cleared and Vincenti pounced.