The champions raced into an early 16-2 lead at Headingley Carnegie with two tries from Ryan Hall and another from Jamie Jones-Buchanan.
Bradford remarkably hit back to claim the lead as Semi Tadulala, Paul Deacon and Steve Menzies scored but the Rhinos found another gear in the closing minutes.
Burrow put the hosts back ahead with a fine individual effort and Scott Donald made sure in injury time after a Lee Smith drop goal.
Second-placed Leeds went into the game looking for revenge after the under-achieving Bulls claimed one of only six league victories this term at their expense in April.
And although Bradford drew first blood with a Deacon penalty in the second minute, Leeds looked like achieving that comfortably as they soon hit their stride.
The Rhinos pounded the visitors' line and broke through after five minutes when Keith Senior, making his 499th professional appearance, powered forward and fed Hall with a smart offload.
Another quickly followed as full-back Brent Webb burst through a gap and the supporting Senior again set up Hall out wide.
Leeds then switched their focus to defence and held firm after conceding two penalties in quick succession inside their own half.
Bradford pressed hard but a promising attack broke down when Paul Sykes dropped the ball under pressure.
That allowed Leeds to come forward again and the hosts took full advantage.
Burrow first won a drop-out after a kick between the posts and then put Jones-Buchanan through from the resulting possession with a delayed pass.
Captain Kevin Sinfield's second conversion put the Rhinos into a comfortable-looking 16-2 lead but Tadulala began the fightback from a seemingly innocuous position.
The Fijian seemed to have few options on the left touchline but was allowed to run unchecked parallel to the line and eventually found a gap to score on the right.
Deacon converted but despite a strong finish to the first half, Bradford went in 18-8 behind at the break after a Sinfield penalty.
Leeds started the second half strongly and Webb, Ali Lauitiiti and Ryan Bailey all went close to forcing their way over.
That proved Webb's last major involvement as he limped off soon after following a heavy tackle.
But Bradford weathered that storm and pulled themselves right back into contention when Deacon went over from close range and converted his own score.
The Bulls sensed an opportunity and Dave Halley was stopped just short after a Tadulala break.
Play was then quickly switched to the left and Menzies levelled the scores by finishing a slick move.
Deacon added the goal to put Bradford ahead 20-18 but that was quickly cancelled out by a Sinfield penalty.
Deacon was off target with another penalty shot and Leeds seized the lead once again through Burrow 13 minutes from time.
The scrum-half deftly beat Michael Worrincy on the right and powered inside to beat the dive of Halley and score by the posts.
Sinfield added the extras but then hit the upright and missed the target with drop-goal attempts as he looked to make the game safe.
His third effort was charged down but Smith quickly gathered and drop-kicked a goal himself.
That broke the Bulls' spirits and Donald charged clear at the end to add a fifth Leeds try.
POST-MATCH COMMENTS
Leeds coach Brian McClennan praised the way his side finished off a dangerous Bradford side in a Friday night Super League derby.
McClennan hailed the determination of the Bulls but was pleased with the way his side finished the job off.
"We got off to a good start but then Bradford came back really well. They got a bit of ball and were very good with it, attacking our line," he said.
"They played well, it was a derby match and they really got up for it. We were really strong in the first 10 and to come back from that was good. I think Bradford did a pretty good job."
"But in the end we came away with a good win. I like the way we finished."
Bradford boss Steve McNamara was left rueing a disallowed Rikki Sheriffe try, who went for the line late on but was adjudged to have been in touch before grounding the ball.
As the clash was not being shown on live television, the referee could not consult the cameras before making his decision.
"He was adamant he scored the try, his technique was great for it," McNamara said.
"That is an extremely tough decision but if there had been a video referee we'd have been a lot clearer. I am a massive fan of the video ref and I wish there had been one here tonight."
McNamara felt that his side could have won the game with a little help from the video referee and claimed that Leeds were flattered by the scoreline.
"We gave ourselves a bit of a mountain to climb but for large parts I thought we were the better side."
"It's a cruel sport. I don't think we got what we deserved tonight. There was some great effort from a lot of players but I am really disappointed we have not won."