John Gorman's side was heading for three more points until a nightmare final four minutes that brought goals for Paul Scott and star striker Simon Whaley.
Scott headed home a Brian Barry-Murphy corner while Whaley netted from six yards after good work and thoughtful play by substitute Stuart Barlow.
Victory avenged a 4-0 mauling at Adams Park earlier in the season prompting manager Chris Casper to say: "They are a good team, no question about it, but I thought we deserved a result.
"Wycombe knew as well as anyone the run would come to an end, I'm just glad it came to an end against us.
"I thought we showed them a bit too much respect in the first half but we were much better in the second and I'm really proud of all my players."
Opposite number John Gorman was among the first to congratulate the Bury team shaking hands with the players at the end of the match. "That's what you expect from someone who has got class," added Casper.
Despite his disappointment Gorman said: "Fair play to Bury, they played with a high tempo in the second half. But I thought we should have had the game won by half-time.
"All good runs must come to an end but it's still hard to take."
Wycombe arrived at Gigg Lane unbeaten since the final game of last season. And when Kevin Betsy shot them in front after 21 minutes it appeared they were on their way to a league double.
Instead, Bury produced one of their best 45 minutes of the season to suggest better times are just around the corner.