The Chiefs came from 20-0 down after 21 minutes to hand the runaway Super Rugby leaders their second defeat of the season after a breathless 80 minutes in the heat of Fiji's National Stadium.
Bottom of the New Zealand conference 26 points behind the double defending champions at the start of the contest, the Chiefs looked destined for defeat when they conceded three unanswered tries in 11 minutes.
Tries from fullback Solomon Alaimalo, hooker Samisoni Taukei'aho and lock Jesse Parete sent them into the break only a point down, however, and better was to come in the second half.
Winger Braydon Ennor stretched the Crusaders lead just after the resumption but the Chiefs, running the ball from everywhere, hit back through halfback Brad Weber and hit the front courtesy of a blistering run from outside back Shaun Stevenson.
Holding a six-point lead with 13 minutes remaining, the Chiefs still eschewed the conservative and replacement back Tumua Manu snatched a 22 dropout out of the air to seal a famous victory with a sixth try two minutes from time.
The last time the Crusaders and Chiefs met, in early March, the Crusaders dealt the Chiefs a thumping 57-28 defeat in Christchurch.
The loss is just the second of the season for the Crusaders, who were beaten 20-12 by the Waratahs in round six. They've struggled in recent weeks, with two draws and a close win over the Blues in their last three games.
The Chiefs have also been inconsistent, beating the Reds 19-13 last week, but losing to the Blues 23-8 the week before.