Alexander celebrates after scoring from the spot in the 42nd minute
Graham Alexander scored a penalty in each half as Burnley made certain of a place in the Championship play-offs.
City striker Nicky Maynard had a goal disallowed for offside before the home struck twice just before half-time.
Alexander converted after Wade Elliott was fouled and Elliott then extended the lead with a deflected 20-yard shot.
Bradley Orr handled to allow Alexander to score his 10th goal of the season after the break and Joey Gudjonsson added a late fourth from close range.
Burnley will now play Reading in the play-off semi-finals as they look to reach the top flight for the first time since 1976.
Manager Owen Coyle must have been delighted with his side's positive start which saw Clarke Carlisle head narrowly over from a corner and Chris McCann test City keeper Adriano Basso from Elliott's right-wing cross.
The pressure was maintained as Chris Eagles rattled the crossbar with a right-footed shot and although Maynard had the ball in the net after a rare City attack, the assistant referee's flag had already been raised.
It looked like the visitors might hold out until the break but Jamie McAllister fouled Elliott and Alexander gave Basso no chance with a firmly struck penalty into the top corner.
Elliott's left-footed strike sent the home fans off for half-time refreshments in jubilant mood.
With City offering only a sporadic threat it was merely a question of whether the Clarets could extend their lead and they duly did so when Orr was penalised for blocking a cross from Eagles with his arm.
Alexander made no mistake from the spot and with the mood of jubilation among the home supporters was taken to new heights four minutes from time when Basso blocked a shot from Eagles and Gudjonsson put away the rebound.
Burnley manager Owen Coyle: "This group of players have played more games this season (58) than anybody except Manchester United and they just keep giving everything they've got.
"Some of the football was outstanding, it was precise passing and movement with pace and all the things that we're good at.
"If we carry that through and replicate it in the two games against Reading then we've got a good a chance.
"We now have two tough games against quality opposition but I think Reading will be saying the same about us.
"They know we can play a little bit and I think you will see two very good footballing sides.
"We're in terrific form and, having sampled the top flight with Bolton as a player, I now want to sample it with Burnley."
Bristol City manager Gary Johnson:
"We're not a bad Championship side but we looked like one at Burnley.
"There was a spell for 20 minutes in the first half where we quietened the crowd a bit. But not for long.
"Once they scored the two goals it was always going to be tough.
"We will now start preparing for next season and begin talking to players about contracts and see who is going to stay with us."
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