Danny Ings came up with a classy late winner to maintain the Clarets 100 per cent start to pre-season.
8 mins: GOAL BURNLEY
10 ANOTHER GOAL
The former Bournemouth striker made it two goals in as many games with just eight minutes remaining of a game of precious few chances.
And it took a moment of cool class from Ings to settle an even contest, as he coolly clipped the ball over Shakers keeper Cameron Belford after bearing down on goal.
The Clarets had earlier come closest to breaking the deadlock through an early Charlie Austin header and a second half piledriver from Keith Treacy.
But the Shakers showed resilience and handed Eddie Howe's men a far sterner test of their credentials than the pre-season curtain-raiser at Altrincham.
And had Steven Schumacher shown more composure in the opening half, the League One side could have claimed a just reward for their efforts.
As it was, Howe was delighted at a clean sheet, another 90 minutes in the tank for the majority of his first team squad and an unbeaten start to take into the two-game tour to Bath next week.
The gaffer handed George Porter his first start since his summer arrival from Leyton Orient, forming part of a three-pronged strike force alongside Junior Stanislas and Charlie Austin.
And it was Austin who had the first chance of the night, heading back across goal from Joseph Mills' superb deep left wing cross and seeing the ball float just over.
But it was Bury who should have taken the lead in the 14th minute when Steven Schumacher blazed over from 12 yards as a cross found him unmarked in the box.
Stanislas was revelling in his role on the left - and after dragging a shot wide from a promising break, he stepped up to take free kick responsibilities when Mills' rampaging run was ended by a foul.
The former West Ham wide man eyed up the opportunity, but curled his 25-yard free kick inches wide of the right hand post with keeper Trevor Carson a bystander.
At the opposite end Brian Jensen, who recently signed a new contract, was back in goal after recovering from a shoulder niggle.
And the Dane made his first meaningful save of the night just after the half hour, getting down well to hold Shaun Harrad's smart shot on the turn.
And an even half came to an end with Porter driving at the heart of the Shakers' defence and firing just wide.
As at Altrincham at the weekend, there were 11 changes at the break as Howe continue to give his entire squad equal match time.
Skipper Jason Shackell was at the heart of a three-man central defensive unit, flanked by Kevin Long and David Edgar, making his first appearance after being given an extended summer break due to his international commitments with Canada.
That left Danny Lafferty and Luke O'Neill operating as wing-backs in an attacking line-up.
But the first scare came in the Burnley defence on the hour mark as Sweeney's whipped corner was flicked on at the near post and Schumacher was a hair's breadth from converting from point blank range as he stretched his neck muscles.
However, the Clarets bounded upfield to create their own glorious chance. Treacy was the architect with a sublime piece of skill to nip inside Phil Picken and his low cross was just too far ahead of the inrushing Paterson.
Treacy went for goal himself midway through the half and his bullet looked destined for the bottom corner, only to be grabbed at full stretch by Carson.
But the Irish wide man again turned provider to tee up Ings for the clincher as the clock ran down.
His raking pass found the Clarets striker and after outpacing the defence Ings bade his time to outfox Belford with the cheekiest of chips.
BURNLEY (first half): Jensen, Trippier, Duff, Mee, Mills; Marney, MacDonald, Wallace: Porter, Austin, Stanislas
Subs: Grant, Edgar, Lafferty Hewitt, Ings, Paterson, Long, Shackell, McCann, O'Neill, Treacy
BURY: Carson, Picken, Skarz, Sweeney, Worrall, Schumacher, Marshall, Harrad, Elford-Alliyu, Sodje, Hughes.
Subs: Lockwood, Bishop, John-Lewis, Carrington, Harrop, Jones, Melia, McLaughlin, Boswell, McCarthy, Belford.
Att: 1,981 (1,116 Burnley)