The Bulls kicked off their Australasian tour with a bonus point 35-41 victory over the Rebels at AMI Stadium in Melbourne on Friday.
The first half of the match was extraordinary as both teams scored four tries each earning them both the four try bonus point.
The Bulls led 28-31 at half time but could not put the Rebels away as they were pushed right to the death.
The Bulls take five points from the match while the Rebels take two points for their four tries and for finishing within seven points.
The result moves the Bulls to the top of the Super Rugby standings after the highly entertaining match.
Both teams scored five tries apiece - four each in the first half -with two Morne Steyn penalties proving the difference.
"I think it was a pretty exciting game for the fans, high intensity and good attack from both sides," Bulls skipper Pierre Spies said.
"It wasn't the best defensive effort from us but it was a good start to the tour and we're happy with the win."
In a scintillating first period, both sides showed their attacking intent from the outset.
The Bulls crossed first when winger Akona Ndungane finished off a backline move to score in the corner, only for the Rebels to hit back almost from the kick-off when giant front rower Rodney Blake barged over.
Melbourne's forwards were holding their own against the much-vaunted Bulls pack and they soon hit the front thanks to a brilliant scything run from flyhalf Kurtley Beale, who split the defence and passed inside to an unmarked Cooper Vuna to score under the posts.
The Bulls regained control as first winger Bjorn Basson and then Steyn went over, before Steyn kicked a penalty after Melbourne's Luke Jones was yellow carded for a dangerous tackle.
The Rebels came again however, with Nick Phipps darting over with six minutes left in the half to close the gap once more.
However, the Bulls set up a rolling maul from a line-out five metres out from the Rebels' line and CJ Stander crashed over to give the visitors a bonus point try three minutes from halftime.
The home side refused to concede and deep into injury time inspirational skipper Gareth Delve crossed under the posts to score the Rebels' fourth try and make it 31-28 to the Bulls at the break.
The second half was always going to struggle to match the first, as both teams began to suffer from fatigue.
It took until the 60th minute for the first score of the second period, but it was worth the wait as Steyn noticed Rebels fullback Richard Kingi out of the line and his deft chip ahead was regathered by centre JJ Engelbrecht.
Just when it looked like the Bulls would run away with the match Vuna scored his second for the Rebels, following up a superb 40 metre break from centre Mitch Inman, who was dragged down centimetres from the line but laid the ball back for his support.
Steyn then gave the Bulls some breathing space with his second penalty and they held on as the desperate Rebels finally ran out of time.
Final Score Rebels 35 (28) Bulls 41 (31).
Tries - R. Blake, C. Vuna 2, N. Phipps, G. Delve
Con - K. Beale 5
Cards - L. Jones (yellow and white)
Tries - A. Ndungane, B. Basson, M. Steyn, CJ. Stander, JJ. Engelbrecht
Pen - M. Steyn
Con - M. Steyn 5
Cards - F. Van der Merwe (yellow)
Referee: Andrew Lees
Assistant Ref 1: Angus Gardner
Assistant Ref 2: Julian Pritchard
1. Nic Henderson, 2. Ged Robinson, 3. Rodney Blake, 4. Cadeyrn Neville, 5. Hugh Pyle, 6. Luke Jones, 7. Tim Davidson, 8. Gareth Delve, 9. Nick Phipps, 10. Kurtley Beale, 11. Cooper Vuna, 12. Lachlan Mitchell, 13. Mitch Inman, 14. Mark Gerrard, 15. Julian Huxley.
Replacements: 16. Adam Freier, 17. Jono Owen, 18. Al Campbell, 19. Ryan Hodson, 20. Richard Kingi, 21. James Hilgendorf, 22. Stirling Mortlock.
15. Zane Kirchner, 14. Akona Ndungane, 13. JJ Engelbrecht, 12. Wynand Olivier, 11. Bjorn Basson, 10. Morne Steyn, 9. Francois Hougaard, 8. Pierre Spies, 7. Jacques Potgieter, 6. CJ Stander, 5. Juandre Kruger, 4. Flip van der Merwe, 3. Werner Kruger, 2. Chiliboy Ralepelle, 1.Dean Greyling.
Replacements: 16. Willie Wepener, 17. Frik Kirsten, 18. Wilhelm Steenkamp, 19. Arno Botha, 20. Jano Vermaak, 21. Louis Fouche, 22. Johann Sadie.