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The Bulls outscored the home side by two tries to one but Carter kept the scoreboard ticking over, punishing the South Africans for conceding a string of penalties in Christchurch.
Zac Guildford scored the Crusaders' only try midway through the first half and the Bulls had left themselves with too much to do by the time Dewald Potgieter and Wynand Olivier touched down in the last 18 minutes.
Last year's runners-up head into next weekend's semi-finals bidding to keep alive their chances of adding to their record seven titles.
The Bulls set out to disrupt the Crusaders from the start but sloppy errors handed the home side some easy early shots at goal for a lead the New Zealanders never looked like relinquishing.
"Especially in that first 40 minutes, we played at the right end of the field and we didn't give them any momentum," Crusaders captain Richie McCaw told Fox Sports.
"I thought we limited our mistakes and discipline was good because they applied pressure."
Carter kicked his side into a 6-0 lead before setting up Guildford for his try, drawing in two defenders on the 22 before slipping a short pass that sent his teammate through the gap.
The wing touched down behind the posts to give Carter a simple conversion.
With the Bulls unable to gain a foothold, Carter then stretched the lead by another three points.
Advantage was being played for an offside when the No. 10 swivelled to pick up a ball he had spilled and dropped a goal with his less favoured right foot.
A long-range Morne Steyn shot at goal which reduced the deficit to 16-3 at halftime was the Bulls' first score in 117 minutes at Rugby League Park, having lost 27-0 last season.
The Bulls returned to the pitch seemingly invigorated after the interval but their fierce tackling only gifted the Crusaders another three points when a late hit on Ellis gave Carter another penalty, which he easily converted.
It was soon 22-3 when Carter smacked over another penalty via the post after he was felled by a high challenge.
Potgieter worked his way over in the corner following a surge from a lineout and Olivier reduced the arrears further but both efforts went unconverted.
Carter subsequently rubbed salt in the wound with his fifth and sixth successful penalties.
Scorers:
Bulls - Tries: Dewald Potgieter, Wynand Olivier. Penalty: Morne Steyn
Teams:
Crusaders:
15 Israel Dagg, 14 Adam Whitelock, 13 Robbie Fruean, 12 Ryan Crotty, 11 Zac Guildford, 10 Dan Carter, 9 Andy Ellis, 8 Richie McCaw (captain), 7 Matt Todd, 6 George Whitelock, 5 Samuel Whitelock, 4 Luke Romano, 3 Owen Franks, 2 Corey Flynn, 1 Wyatt Crockett
Substitutes: 16 Quentin MacDonald, 17 Ben Franks, 18 Tom Donnelly, 19 Luke Whitelock, 20 Willi Heinz, 21 Tom Taylor, 22 Sean Maitland
Bulls:
15 Zane Kirchner, 14 Akona Ndungane, 13 JJ Engelbrecht, 12 Wynand Olivier, 11 Bjorn Basson, 10 Morne Steyn, 9 Francois Hougaard, 8 Pierre Spies (captain), 7 Dewald Potgieter, 6 Jacques Potgieter, 5 Juandre Kruger, 4 Flip van der Merwe, 3 Werner Kruger, 2 Chiliboy Ralepelle, 1 Dean Greyling
Substitutes: 16 Willie Wepener, 17 Frik Kirsten, 18 Wilhelm Steenkamp, 19 Deon Stegmann, 20 Jano Vermaak, 21 Louis Fouche, 22 Francois Venter
