Andrew Clark's rebound goal from the slot at 11:39 of sudden-death overtime lifted the Thunder to victory.
Idaho turned a 3-1 third period deficit into a 3-3 tie thanks to two Adrian Foster goals. The Steelheads were unable to convert on 1:57 of power play hockey before the regulation buzzer and the game went to overtime.
"We were battling, we got back in the game and I thought we were feeling good," Foster told reporters after the game. "We've got to be better the first 60, clean some things up. I know we've got it in our room."
Head coach Brad Ralph, clearly frustrated with the first two games of the series said he has well-placed confidence in his hockey team.
"This series is far from over. We played a heck of a game here tonight (Sunday) and Friday night I think we deserved a better fate, but that's why we play a seven-game series," Ralph said.
"We're a heck of a hockey team and we will bounce back."
Game 5 is Wednesday starting at 8 p.m. in Stockton.
CableOne will air the remaining road playoff games on channel 17. The Steelheads will also host watch parties in CenturyLink Arena's SportsZone.