The Blues staved off a second half fightback from the Rebels to claim a 36-32 victory in Auckland on Saturday.
The home side laid the foundation for this win in the first half, when they ran in five tries, with right wing Frank Halai leading the way with a deserved hat-trick.
The opening minutes were highlighted by several errors at the breakdown from the Blues. James O'Connor had an opportunity to open the scoring from the kicking tee twice inside the first five minutes but he missed both penalty attempts.
Blues goal-kicker Chris Noakes also missed a shot at goal, shortly afterwards, but Halai scored the game's opening try in the 10th minute after Angus Ta'avao did well to draw in a defender before offloading to the flyer.
Noakes missed with the conversion attempt and his poor start to the game got even worse when he missed a vital tackle on Mitch Inman which allowed the Rebels centre to score the visitors' first try two minutes later.
The Blues restored their lead, in the 18th minute, when Francis Saili clung to a brilliant Rene Ranger offload on his bootlaces, before kicking ahead and beating the cover defence in a race to the ball behind the Rebels' try-line.
Five minutes later Halai got in for his second try after running onto a long pass from Charles Piutau before Scott Higginbotham struck back with a five-pointer for the visitors after shrugging off a sluggish tackle from Ali Williams.
Halai secured his hat-trick in the 31st minute after Ranger put him in the clear with a perfectly-timed long pass inside the Rebels' 22. The big wing still had work to do and stepped out of a tackle from Cooper Vuna before touching down.
The Rebels suffered a major setback midway through the half when, first, O'Connor was forced off with a chest injury, and then his replacement Angus Roberts also cried off with a dislocated shoulder after spending only six minutes on the field.
The Melbourne-based outfit started the second half brightly and after Jarryd Saffy and Cadeyrn Neville were both held up over the try-line they were eventually rewarded, in the 46th minute, when Lachlan Mitchell crashed through a tackle from Ranger before dotting down.
The visitors were dominant for the next 20 minutes, scoring a further 10 unanswered points through another Inman try - after Higginbotham took a quick tap penalty close to the Blues' try-line - and a conversion and a penalty from Jason Woodward.
With the score at 29-25 to the hosts, the Rebels were brimming with confidence but Ranger took the wind out of their sails when he burst through a gap in their defence, at a ruck, to score the hosts' sixth try.
To their credit, the Rebels did not surrender and they clinched their second bonus-point - for losing by less than seven points - when Woodward scored another try, which he converted in injury time.
Tries: Halai 3, F Saili 2, Ranger
Con: Noakes 2, Kerr
Tries: Inman 2, Higginbotham, Mitchell, Woodward
Con: Woodward 2
Blues:15 Charles Piutau, 14 Frank Halai, 13 Rene Ranger, 12 Francis Saili, 11 George Moala, 10 Chris Noakes, 9 Piri Weepu, 8 Peter Saili, 7 Brendon O'Connor, 6 Steven Luatua, 5 Ali Williams (c), 4 Anthony Boric, 3 Angus Ta'avao, 2 Quentin MacDonald, 1 Tim Perry
Replacements:16 Gafatasi Su'a, 17 Ofa Tu'ungafasi, 18 Ronald Raaymakers, 19 Luke Braid, 20 Jamison Gibson-Park, 21 Baden Kerr, 22 Lolagi Visinia.
Rebels: 15 Jason Woodward, 14 Tom English, 13 Mitch Inman, 12 Lachie Mitchell, 11 Cooper Vuna, 10 James O'Connor, 9 Nick Phipps, 8 Scott Higginbotham (captain), 7 Scott Fuglistaller, 6 Jarrod Saffy, 5 Cadeyrn Neville, 4 Hugh Pyle, 3 Laurie Weeks, 2 Shota Horie, 1 Nic Henderson.
Replacements: 16 Ged Robinson, 17 Paul Alo-Emile, 18 Luke Jones, 19 Gareth Delve, 20 Nic Stirzaker, 21 Angus Roberts, 22 Bryce Hegarty.
Referee: Garrat Williamson