In the scorching heat, the Blues went down by three tries to two, much to the disappointment of the majority of the 25,112 fans at Eden Park.
The four competition points gained through the win lifted the 2010 champions into second place behind the Brumbies, who are the only other undefeated team after four rounds.
A pair of tries, to wingers Lionel Mapoe and Akona Ndungane, ensured the visitors were in front at half-time after Blues fly-half Baden Kerr had put his side up with two penalty goals earlier in the match.
The second half saw a brief fightback from the Blues, who regained a one-point lead thanks to full-back Charles Piutau's try.
But it was not to be as the Bulls hit back immediately with a try of their own from Arno Botha.
The result could have been different when Rene Ranger dotted down late on, but a Morne Steyn penalty had already put the visitors too far ahead.