Rene Ranger's individual try with four minutes to go narrowed the gap to 25-21 and set the match up for a barnstorming finish.
Although they responded well to their early setbacks, there was a sense of what might have been for the Blues.
Another couple of eyebrow-raising decisions from Kirwan was his replacing of halfback Piri Weepu and prop Charlie Faumuina, just as the Blues were beginning to get a toe-hold in the game.
The Bulls' win, their first at Eden Park, represented a South African trifecta over New Zealand teams this weekend after the Cheetahs beat the Highlanders and the Stormers beat the Chiefs.
All victories were based on forward power - set piece dominance - and taking charge of the collisions.
For the Blues, loosehead prop Tim Perry, of Tasman, was making his debut. Baden Kerr, in only his second Super Rugby match, took over from the in-form Noakes. Waisake Naholo, on the left wing, was also making his debut. Taranaki flanker Kane Barrett got the nod for his first Super Rugby match, Steven Luatua moving to No8.
It was a tough day for all, although they didn't disgrace themselves.
The Bulls took a 15-6 halftime lead through tries to their wings Lionel Mapoe and Akona Ndungane. No8 Pierre Spies went close for a third as the half counted down.
Mistakes were common among the Blues as they tried to make something happen. Charles Piutau was dangerous from the back. Centre Rene Ranger injured a shoulder in the first half but bounced back superbly.
The sight of Liaki Moli climbing over a maul was entertaining, but a symptom of his team's ill discipline.
He later dropped the ball when his team launched an attack, and was then penalised for a high tackle.
In the second half, all change. Frank Halai's leg drive put the Blues close and Piutau finished on the left, converted by Kerr. The Blues were back in the lead but straight away the Bulls responded through flanker Arno Botha, who scored after extraordinarily good handling skills from reserve prop Werner Kruger, who juggled the ball by his laces.
Halfback Jano Vermaak went agonisingly close for the Bulls in the right corner, only to drop the ball, before Ranger's long-range stunner.
A Steyne penalty on fulltime sealed it for his team.
Blues (Charles Piutau, Rene Ranger tries; Baden Kerr con, 3 pens)
Bulls (Lionel Mapoe, Akona Ndungane, Arno Botha tries; Morne Steyn 2 cons, 3 pens)
HT: 15-6.