Clarke Carlisle's last gasp overhead kick earned the Clarets a sensational point after a remarkable second half at Ashton Gate.
Burnley looked to have ended City's unbeaten start to the season with a goal six minutes after the break from Andy Gray, celebrating his 50th league appearance for Burnley.
City sub Darren Byfield then bagged a brace in the last ten minutes to transform the game and give home fans belief they would earn all three points.
However, with almost the last kick of the game, Carlisle bagged his first goal for the Clarets with a stupendous overhead kick.
The Clarets named an unchanged 16, including the same starting 11 that earned a midweek victory at Sheffield Wednesday.
As in recent weeks, Burnley began brightly on their first visit to Ashton Gate since 1999.
Unbeaten City, who have enjoyed two spells at the top of the Championship since earning promotion in the summer, were clearly looking to playmaker Lee Trundle to unhinge Burnley's rearguard.
The former Swansea striker was anchored on the right flank up against Stephen Jordan and early tussles suggested this battle would be key.
City forced quickfire corners with a quarter hour gone, but Gabor Kiraly cleaned up neatly to avert any danger.
The Clarets suffered a blow early in the game when Chris McCann fell heavily under a challenge and was stretchered from the field to be replaced by Joey Gudjonsson.
The cagey start continued until Marvin Elliott headed City's first chance wide of the far post midway through a scrappy half.
Kiraly again snuffed out the danger seven minutes before the break, diving on the ball following a spot of ping pong in the Burnley box.
And with the half time whistle approaching Kiraly made another routine save, springing to his right to hold Michael McIndoe's weak header after the City midfielder sneaked in on the blind side.
But the interval arrived with no further action.
John Spicer replaced Kyle Lafferty at the break, in turn making his 50th appearance for the club.
Immediately, Burnley were sparkier in attack and the opening goal duly arrived in the 51st minute.
Robbie Blake was the creator with a chip to the back post that was only half cleared to Elliott. The winger smashed a shot off the inside of the left hand post and goal poacher Gray was perfectly placed to slot home the rebound.
Blake weaved his way into the City box on the hour mark, but crucially failed to find a shot to match his mazy run.
Former Claret loanee Bradley Orr was woefully off target with a drive from distance as the Robins desperately sought a quick reply.
But Gudjonsson was close to sealing the victory three quarters into the game with a fierce low drive that fizzed narrowly wide of Basso's post.
Former Ashton Gate favourite Ade Akinbiyi was given a 15 minute run out for Blake as Burnley looked for the striker's fresh legs to stretch the Bristol back line.
But it was City sub Darren Byfield who grabbed the lifeline for the home side, heading home with ten minutes to go after Burnley could only half clear the danger.
Clarke Carlisle eased the pressure with two terrific last gasp clearances as rejuvenated City went in search of a late winner.
But the Clarets could not stem the tide and after Kiraly parried Orr's shot from the edge of the box, former Millwall striker Byfield pounced
However, there was to be a sting in the tail and after Akinbiyi kept the ball alive in the City box, Carlisle leapt to acrobatically earn the Clarets a deserved point.
Burnley: Kiraly, Duff, Carlisle, Caldwell, Jordan, W Elliott, Alexander, McCann (Gudjonsson 19), Lafferty (Spicer 45), Blake (Akinbiyi 75), Gray
Subs: Unsworth, Jensen.
Booked: Duff 38, Gray 90
Bristol City: Basso, Orr, Fontaine, Carey, McAllister, Wilson (Byfield 45), Johnson, M Elliott, McIndoe, Trundle, Sproule (Vasko 79).
Subs: Weale, Murrey, Skuse.
Booked: Trundle 76
Ref: M Thorpe
Att: 14,079 (989 Burnley)
