The Golden Knights seized a 2-1 edge in the NHL's best-of-seven championship series with Game 4 set for Tuesday, also in Las Vegas.
Theodore, who leads all defensemen with six playoff goals, got a measure of redemption after his penalty late in the third period set up Carolina's equaliser after Vegas led 4-0.
"That can't happen again," said Theodore.
"Defensively, we have to be sharper. I fired that puck out of play with three minutes left. That's on me. I was fortunate to get it back there in overtime."
Theodore's off-target shot struck the boards behind the goal, but the puck bounced off the stick of Carolina's Jordan Martinook and struck the back of Hurricanes goaltender Brandon Bussi's left foot, then slid into the net.
"There were a lot of pucks bouncing everywhere," Theodore said.
"I like the resiliency of our group. I like the way we started the second overtime, and I thought we were playing more on our toes."
Vegas star Mitch Marner scored the fastest hat-trick in Stanley Cup Final games in only six minutes and 10 seconds as Vegas stormed to a 4-0 lead.
After Tomas Hertl netted a power play goal in the second period for a 1-0 lead, Marner took control.
Marner scores fastest final hat-trick
His first goal came off a deflection, the next on a backhand shot and the third with a blast from the right wing off the far post
Marner's three goals in 6:10 broke the former fastest final hat-trick of 6:21, set 69 years ago by Montreal legend Maurice Richard.
Marner had only the second natural hat-trick - three consecutive goals - in one period in final history, the other was by Ted Lindsay in 1955.
And it was the first one-period Cup Final hat trick since Peter Forsberg in 1996.
Carolina switched to backup goalie Bussi in the third period, and he stopped Marner on the first Cup Final penalty shot in 19 years.
Bussi then watched the Hurricanes score three goals in 39 seconds, another Stanley Cup Final record, to put the game on a knife-edge at 4-3.
Martinook scored 7:03 into the third period, Taylor Hall scored 26 seconds later, and Jordan Staal netted a tip-in 13 seconds after that.
Theodore's delay of game penalty set up Andrei Svechnikov's power play equaliser with 1:42 remaining to take it to overtime.
The 28 playoff points by Marner this season are the most in NHL history by any player in his first campaign with a team, the 29-year-old Canadian arriving last year in a sign-and-trade deal from Toronto.
Marner passed along any praise to his linemates.
"Can't do it by myself, that's for sure," Marner said. "All five guys have been on a great page. I like our line's game a lot."
The Golden Knights won their sole NHL crown in 2022, the Hurricanes in 2006.
"We've got to just keep going, keep playing the same way we are, keep being aggressive, and when we get our chances, try and keep capitalising," Marner said.