South Africa striker Tokelo Rantie looked to have sentenced the second-placed Clarets to only their fourth defeat of the season after heading Bournemouth in front early in the second half.
Treacy then bagged his second goal of the season 23 minutes from time to maintain Burnley's unbeaten run dating back to Boxing Day.
Referee Graham Scott carried out a 7.30am pitch inspection before deciding the game could go ahead, but most of the 10,422 crowd must have wished he had called it off after a dire first half.
Defender Simon Francis's long-range effort smothered by Burnley goalkeeper Tom Heaton was the only meaningful attempt from either side before the interval.
It had also required an impressive last-ditch tackle from Francis to stop Bournemouth old boy Sam Vokes latching onto Kieran Trippier's floated cross-field pass in the 17th minute.
The second half was much more entertaining and it took Bournemouth just six minutes after the re-start to take the lead.
Rantie has struggled to justify the club record £2.5million the Cherries paid to sign him from Swedish side Malmo but he completed a home and away goalscoring double against Burnley.
Ian Harte floated in a pinpoint right-wing corner and Rantie rose unchallenged to head past the helpless Heaton and claim his third goal of the season.
Clarets boss Sean Dyche responded to his team falling behind by making a double change, bringing on Treacy and Ross Wallace in place of the ineffective Michael Kightly and Scott Arfield.
The move paid off in emphatic fashion when the two substitutes combined to level the score within six minutes of being called upon.
Wallace broke down the right and his cross-cum-shot deflected kindly into the path of Treacy who lashed the ball into the roof of the net at the far post.
Burnley were indebted to former Manchester United trainee Heaton for denying Bournemouth twice in quick succession in the 74th minute.
First Heaton saved bravely at the feet of Lewis Grabban from a tight angle after the Bournemouth striker had sprinted past full-back Trippier down the left wing.
Seconds later Heaton produced a brilliant fingertip save to turn Tommy Elphick's header over the bar after fellow defender Stephen Cook had nodded Harry Arter's corner across the six-yard box.
Substitute Yann Kermorgant caused the travelling Burnley fans another moment of anxiety soon after replacing goal hero Rantie, with a 20-yard free kick which sailed just over.
Burnley were rescued by the woodwork four minutes from time when Francis's drilled shot from just inside the penalty area clattered the crossbar.