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Cruden pounced on a pass from Crusaders centre Ryan Crotty in the 56th minute, juggled it momentarily, then dashed 40 meters for a try that gave the Chiefs a 20-9 lead after they had trailed 9-3 at halftime.
Winger Lelia Masaga scored an extraordinary solo try six minutes earlier to spark a run of points that propelled the Chiefs into the final against the winner of Saturday's second semi-final between South Africa's Bulls and the ACT Brumbies of Australia.
The Chiefs, defending their first Super Rugby title, came into the match as underdogs despite finishing on top of the New Zealand conference and the overall tournament standings.
They split their two regular-season matches with the Crusaders, but were beaten 43-15 by their Christchurch-based opponents when the two teams met three weeks ago.
The Crusaders carried that momentum into a 38-9 quarterfinal win over the 2011 champion Queensland Reds and were strongly backed to progress toward their eighth Super Rugby title, and first since 2008.
They made a strong step toward that goal when they led 9-3 after a physical first half that was played at exceptional pace but in which the only points came from penalties - three to Crusaders first five Dan Carter and one to Cruden.
Carter missed penalties on either side of halftime, and Cruden narrowed the margin to 9-6 with his second penalty in the 45th minute.
Then Masaga scythed through some hesitant defence to score the Chiefs' first try in the 50th minute, giving them their first lead of the match at 12-9.
Six minutes later, Cruden latched onto Crotty's pass, after the centre turned his back on the defence, and scored under the posts to give the Chiefs an 11-point margin.
They needed every point of that lead in an intense and frenetic last quarter in which the Crusaders put the Chiefs' defence under constant pressure.
They probed every inch of the defensive line for an opening to add to the try scored by fullback Israel Dagg in an almost immediate response to Cruden's score.
But as both teams went to their reserves benches, hoping to find an edge with fresh legs, the Chiefs' defence remained rigid and unyielding.
They hurled back waves of Crusaders' attacks and forced vital turnovers, the last after the final siren which allowed them to clear to touch and end the game.
"A lot of grit," Chiefs captain Craig Clarke said. "A lot of defence that epitomized how deep we can dig. We made it a little bit hard for ourselves with our set-piece. We had to simplify things (in the lineout) and maybe just win a bit of ball at the front with big Brodie (Retallick), and we did that a little bit.
"We managed to hold a bit of possession, but I must mention the way they came back into the game. We were up by 11, and that's a credit to how good they are that we had to dig so deep."
The Crusaders were marginally the better team in a first half in which neither side managed to find an opening.
The Chiefs' lineout struggled early and the Crusaders began to apply pressure in scrums, on one particular occasion near halftime hurling the Chiefs off their ball with a second shove that captured a tighthead.
But the Chiefs were able to regroup at the interval and to play with more precision in the second half.
Clarke decided to forego a close-range penalty shot in the 50th minute in favour of a lineout.
The Chiefs captured their own ball and, after three phases during which they couldn't bend the Crusaders' defence, a long ball allowed Masaga to brush off three ineffective tackles to score.
Cruden then snared the intercept that turned the narrow Chiefs lead into a pivotal advantage.
He converted both tries and ended with 15 points. Dagg scored from the kickoff that followed Cruden's try, running wide in the backline and outflanking defending winger Asaeli Tikoirotuma.
Carter converted from the sideline, finishing with five goals from seven attempts.
But his last shot at goal, a dropped goal attempt in the 76th minute, sailed wide of the posts.
"It's incredibly disappointing," Crusaders captain Kieran Read said.
"We came here wanting to get the goods and it's disappointing, but you've got to give it to the Chiefs. It's their moment and they're doing it well.”
"I guess there are moments in these games that turn them and they got those. Possibly, we could be a bit more clinical. I thought we'd done enough but we didn't get what we needed."
Chiefs 20 (Lelia Masaga, Aaron Cruden tries; Aaron Cruden 2 conversions, 2 penalties), Crusaders 19 (Israel Dagg try; Dan Carter conversion, 4 penalties). HT: 3-9.