Corey Flynn opened the scoring for the visitors within seconds of the start in the capital.
In a replay of the 2006 final, the dethroned champions withstood a yellow card to Mose Tuiali'i in the closing stages to triumph.
The Canterbury outfit had established a a 17-3 lead by half-time after Flynn's score, a first Crusaders try for former Blues lock Ali Williams and three successful kicks from Daniel Carter.
Jimmy Gopperth's penalty was the only home score of the opening period, with Piri Weepu doubling the tally within three minutes of the restart.
Carter extended the visitors' advantage five minutes later with another penalty.
The hosts' pressure resulted in Tuiali'i's dismissal with 15 minutes to go, and New Zealand hooker Andrew Hore capitalised with a try a matter of seconds later.
Gopperth converted, but no further scoring meant the Crusaders went back over the Cook Strait with four vital competition points.