Canterbury went on an 8-0 run in the first two minutes of the second quarter.
The offensive struggles continued for Hawke's Bay as they struggled to make shots inside over Rams bigs Mike Karena and Matthew Moyer.
Canterbury's zone defence was suffocating, holding the Hawks to 10 makes on 30 two point field goals in the first half to lead 41-38 at the big break.
A quick start to the second half saw Hawke's Bay score four straight and claim their first lead since the first quarter.
Both teams found more offensive success in the third but a dry spell for the Hawks saw Canterbury open up another six-point lead with four minutes remaining in the quarter.
Three pointers to Ethan Rusbatch and Jordan Hunt got Hawke's Bay back within touching distance but the Rams answered to lead 66-61 into the fourth period.
Jarrod Kenny hit a long bomb to tie the game just 73 seconds into the deciding term.
The teams traded leads down the stretch and both sides missed free throws that could have given them some breathing room.
Rams guard Taylor Britt found himself wide open from three and hit the shot that put Canterbury up by four with just over a minute remaining.
A huge block from Tajuan Agee allowed Hyrum Harris to tie the game at 82-all, sending the game to overtime.
The Tall Blacks point forward was massive for the Hawks on both ends, brilliantly stealing a Rams inbound pass and finding Jordan Hunt for an and-one layup to put Hawke's Bay up by five.
They didn't look back, outscoring Canterbury 13-5 in the overtime period.
Harris led all scorers with 25 points (10-15 shots), grabbed 11 rebounds, and blocked four shots to drag the Hawks into the playoffs.