Chairboys boss Paul Lambert will wonder long and hard how his team failed to take all three points.
They were excellent value for their 2-0 lead with Andy Bishop mustering only one shot in reply for the home side.
Indeed, Bury couldn't cope with Argentinian midfielder Sergio Torres.
Wanderers should have been in front before Torres latched onto Scott McGleish's pass to score after 14 minutes as McGleish himself was guilty of a miss from 12 yards.
But Torres showed him how to finish, though his task was made easier as Darren Randolph hared off his line when he should have exercised more caution.
Bury then complained bitterly that debutant Leon Knight had dived to win a 37th minute penalty.
McGleish stepped up to notch his eighth goal in as many games, sending on loan Randolph the wrong way.
Bury were not much better at the start of the second half.
Russell Martin fizzed a free-kick narrowly wide while Frank Fielding remained virtually redundant at the opposite end.
However, the game changed when referee Jon Moss awarded his second spot-kick of the night.
This time Martin handled and Bishop tucked away his 17th of the campaign after 63 minutes.
As Bury pressed forward for their first home win under new boss Alan Knill, Wycombe almost sealed the win in spectacular fashion.
Torres clipped a chip towards goal and Randolph atoned for his earlier mistake by pushing the ball onto the crossbar.
It proved a turning point as, two minutes from the end, Dave McCracken was pulled up for handball.
Dead ball specialist Barry-Murphy accepted responsibility and curled a great left-foot shot into the top corner.