The Clarets handed the initiative to Birmingham City in the chase for a play-off spot as they suffered only a second league defeat of the year.
Burnley couldn’t build on a superb early strike from Rob Harker as a missed second-half penalty cost them dearly at Ashton Gate.
Jordan Cropper fired over from the spot with the chance to restore the Clarets’ lead and Bristol City struck twice more to end their losing run as they hung on after Dan Agyei did convert a penalty in the last minute.
And the dropped points mean the Clarets now trail second-placed Birmingham on goal difference with three games to go in in the Professional Development League’s northern section with the top two finishers going into the title play-offs.
The Clarets’ last away trip had ended in defeat for an inexperienced side at Ipswich at the start of the month and they once again came unstuck at the hands of southern group opposition.
But this one will have been more painful after squandering the chance to firm up their position in second place behind group winners-elect Leeds United, who Burnley face in the Premier League Cup quarter-finals on Friday.
Steve Stone’s side couldn’t have asked for a better start thanks to one of the goals of the season from Harker (above).
There were only two minutes gone when the striker collected a headed clearance from Scott Wilson with seemingly little on.
But after taking a touch and carrying the ball sideways, he opted to go for goal and from fully 40 yards sent a stunning effort over City keeper Will Buse and in just under the bar.
The Clarets looked totally in control as Agyei twice went close to doubling the lead, nodding over the top from a corner and then forcing Buse into a save after Bobby Thomas and flying winger Tunde Bayode had opened up the City defence.
But what had the look of a potentially comfortable afternoon took on a different view when a youthful City side – on the back of three successive league defeats – equalised after 20 minutes.
Sam Bell had just offered a warning shot when he got in behind the Clarets’ defence before slipping as he shaped to shoot.
But that wasn’t heeded and moments later Bell did make it 1-1 when Jayden Ali’s flick released him to lift the ball over goalkeeper Aiden Stone.
Dan Agyei kept his scoring run going
The Clarets should have been kicking themselves and were unable to restore their lead before the break, top scorer Agyei again going closest with a fierce drive Buse got down well to save.
The frustration continued at the start of the second half as the visitors wasted the chance of another flying start before falling behind in a disastrous five-minute spell.
Agyei again caused problems to earn a penalty when he was tripped by Joe Low two minutes after the re-start.
But Jordan Cropper blasted the spot-kick over the bar and almost immediately the Robins made the most of the let-off to go ahead when Bell was left in space to hook home his second of the game.
The Clarets - struggling to regain their early stranglehold - looked to respond with Marley Blair sending an effort just wide on the break and a fine save from Aiden Stone to deny Tom Richards at the other end kept the deficit at a single goal.
But the Robins were growing in confidence and after Stone had kept out another effort from Richards, they added a third after 66 minutes, Marcus Day thumping home a superb long-range volley.
Burnley needed a response and Agyei almost provided it, controlling a Blair cross before being denied by Buse’s block as he looked to poke the ball home.
Agyei then fired over with 12 minutes to go as the Clarets looked to launch a fightback.
And when he did find the net in the last minute, slotting home the penalty after Mitch George’s cross had been handled, there was not enough time to rescue a point as Blair saw an effort save by Buse from Burnley’s last-ditch effort to avoid defeat.
Burnley: Stone; Cropper, Thomas, Wilson, Glennon; Blair, Howarth, N’Guessan, Bayode (George 56); Harker, Agyei. Substitutes: Calderbank-Park, Chakwana, Clarke, Harris.
Bristol City: Buse; Turner-Williams, Low, H Smith, Soady; Z Smith; Rees, Ali, Richards, Day; Bell (Conway 85). Substitutes: Pearson, Robertson, James Taylor, Jamie Taylor.
Referee: Scott Jackson.