Aside from a pair of well-crafted counter-attacking tries to Mils Muliaina and Liam Messam in the first half, the Chiefs seemed afflicted by the same malaise that saw them produce such a poor performance last week in Perth.
Their lineout was in disarray, they were making uncharacteristic errors and the Bulls looked like they would consign the champs to consecutive defeats for the first time in almost a year.
But Anscombe and co had other ideas. The replacement fullback sparked the resurgence in the 70th minute, combining brilliantly with fellow substitutes Tim Nanai-Williams and Augustine Pulu to cover the length of the field and grab what appeared nothing more than consolation.
But, after Matt Symons grabbed a bonus-point try from a lineout variation, the Chiefs were left with one final chance to grab an unlikely draw.
They had already strung together a dozen phases inside their own half as the clock ticked into the final minute, before Asaeli Tikoirotuma burst away from a ruck and found support from Andrew Horrell. The centre was brought down short of the line by the frantic cover defence, but his popped pass found Cruden who dove for the corner and barely grounded the ball across the line.
It was heart-racing stuff, seeing the Chiefs sneak ahead of the Blues atop the New Zealand conference, and it would have gone some way to easing the pain of another sub-par performance.
Coming into the clash, it was clear where the Bulls would try to exert their influence over the champs. The Chiefs knew their lineout would be targeting but knowledge and the ability to utilise it are separate propositions.
Rated by most statistics as the best and worst lineout sides in the competition, that disparity was clear in a scrappy opening spell. The Chiefs dominated many facets but the one area in which they were lacking was letting them down.
They led by one point at the break, with three lineout losses costing them on the scoreboard. After two miscues produced a penalty for the Bulls, Victor Matfield sensed a weakness kicked for the corner, forming an unstoppable rolling maul and allowing Deon Stegmann to score.
Another lineout error right on the hooter - the second straight caused by a long throw from Rhys Marshall - gave Jacques Poltgeiter the chance to make it 15-14 heading to the sheds.
The Bulls' physicality helped the home side to take control of proceedings in the second spell. Such was their supremacy, the Bulls set up another rolling maul from the 22, eventually earning a penalty try and a yellow card for Symons.
And after Bjorn Basson was allowed to regather his own grubber to score his side's third try, there appeared only one possible result. Looks can be deceiving, though.
Bulls 34 (Stegmann, penalty try, Basson tries; Potgeiter 5 pens, 2 cons)
Chiefs 34 (Muliaina, Messam, Anscombe, Symons, Cruden tries; Cruden con, pen; Anscombe 2 cons)
HT: 14-15
