The Clarets face a two-week break to lick their wounds after Bristol City's first home win of the season left Eddie Howe's men treading water in the Championship table.
Ross Wallace's equaliser early in the second half gave Burnley hope of a fourth away success of the campaign as Wallace became the first Burnley player since Gareth O'Connor six years ago to score in four successive League games.
But familiar defensive frailties saw improving City hit back with two goals in the space of 13 minutes as substitute Brett Pitman, a prolific scorer under Howe in their time together at Bournemouth, and Albert Adomah struck to give new manager Derek McInnes his first victory at Ashton Gate.
The result made it successive Championship defeats for the Clarets for the third time this season and, unlike on the previous two occasions, Howe will probably welcome this international break to make some running repairs to a squad still not firing consistently on all cylinders.
Brian Easton's return from injury at left-back meant one change to the side that lost in mid-week to Leicester, with Andre Amougou dropping to the bench.
And the Scot made one vital early contribution with an excellent covering tackle to thwart Adomah as he closed in on goal after running into a lofted pass from Neil Kilkenny.
Jay Rodriguez goes close with an early chance
That came just moments after Nicky Maynard had put an effort just wide at full stretch and Jay Rodriguez had almost struck at the other as a period of jousting ended with a flurry of chances.
The first had come Rodriguez's way, but after opening up the City defence with a clever one-two with Charlie Austin, the striker didn't get enough on his angled shot to beat David James as the former England keeper pushed the ball round the post.
Austin was then denied by a last-ditch tackle from Cole Skuse but Bristol, with only four goals previously at Ashton Gate all season, continued to look a threat and Grant had to get down smartly after half an hour to save from Adomah.
That was nothing, though, on the block he made from Stephen Pearson moments later after he spread himself to outfox his former Derby County team-mate on the on-loan midfielder's debut.
Despairing dive from Lee Grant as City go 1-0 up
And with Grant quickly becoming a central figure, the keeper then plunged to his left to keep out a low drive from Marvin Elliott as the Clarets battled to stay on level terms.
Austin, a constant nuisance to the home defence, almost relieved the pressure when he pounced on a mistake from Skuse to steer an effort just wide from a decent chance after Keiran Trippier's long ball was not dealt with by the City full-back.
But three minutes before the break the Robins found a way through to go 1-0 up.
Elliott met Ryan McGivern's cross with a downward header which didn't look overly threatening until Pearson got a touch to help the ball on and then shepherd it over the line and into the bottom corner of the net.
The Clarets needed a response and it came as quickly as the 48th-minute as Wallace pounced to continue his purple patch.
Ross Wallace makes it 1-1 and celebrates another goal
McGivern's poor clearance gave Trippier the chance to put City's defence back under pressure and when Junior Stanislas fed Wallace, the winger out-thought James to float a left-foot shot into the roof of the net from ten yards out.
Apart from an Adomah shot which Grant beat away, the Clarets looked capable of going on to take control as they then enjoyed their best spell of the game.
But not for the first time this season, Howe's men were then suddenly undone at the back and left with it all to do again with half an hour to go.
Adomah's mis-cue from Maynard's pull-back looked to have left the Clarets off the hook but, too slow to react to the second phase, Pearson was allowed to cross for Pitman to ram the ball home from inside the six-yard box.
Burnley countered with a Rodriguez header at James and with time beginning to run out, Howe sent on Keith Treacy to try and engineer an equaliser.
But the substitute hadn't had a touch by the time City broke clear to seal their long-awaited first home success.
But City's third goal on the break kills off the Clarets
Clearing a Wallace free-kick, the Robins countered at speed with Kilkenny picking out Adomah to race clear and finish impressively with a strike across Grant from the edge of the penalty area.
Rodriguez's radar wasn't quite as finely tuned as he sent a low drive just wide four minutes later and with that any chance of a late fightback disappeared, even Treacy's thundering injury-time strike unable to ruffle the Robins' feathers as James made a fine save to send Burnley home empty-handed.
Burnley: Grant, Easton Mee, Edgar, Trippier, Wallace, McCann (Hines 80), Bartley (Marney 86), Stanislas (Treacy 72), Rodriguez, Austin. Subs: Amougou, Stewart.
Booking: Wallace 76, Edgar 87
Bristol City: James, Skuse, Fontaine, Nyatanga, McGivern, Adomah, Elliott, Kilkenny, Pearson (Cisse 72), Bolasie (Pitman 54), Maynard (Woolford 83). Subs: Wilson, Gerken.
Booked: Pitman 76
Referee: Gary Sutton
Attendance: 12,187 (Burnley 666)