Theodore scored on a power play with a snap shot through a screen provided by William Karlsson and Mark Stone five seconds after J.T. Miller was called for hooking.
"It's crazy," Theodore said. "I think we had so many good quality chances. I thought we did a lot better job getting to the net tonight, getting rebounds, so to finally break that tie was huge. It was a big one for our group."
WATCH: [All Canucks vs. Golden Knights highlights]
Robin Lehner made 14 saves for his third shutout of the series for Vegas, the No. 1 seed in the West, which advanced to the conference final for the second time in three seasons.
"Robin Lehner was great; we didn't have any passengers tonight," Golden Knights coach Peter DeBoer said. "We had 20 committed guys out there making sure we advanced. We felt like we played two pretty good games in Games 5 and 6, and it took almost all of Game 7 in order to put them away, so you have to give (Canucks coach) Travis Green and his group a ton of credit for how they battled and hung in there and pushed us right to the edge."
Game 1 of conference final will be against the Dallas Stars in Edmonton, the hub city for the conference finals and Stanley Cup Final, on Sunday (8 p.m. ET; NBC, TVAS).
Thatcher Demko made 33 saves for the Canucks, the No. 5 seed, who were 0-for-4 with 11 minutes of power-play time.
"Man, did [Demko] ever give us a chance," Green said. "I'm happy for him. I've been with him for a while. It was good to see him raise to this level. I don't think many people thought we'd be a goal away from going to the (NHL) semifinals.
"[Vegas] is a big, strong, fast team and I know we left everything out there. Our guys were coming off the ice panting and tired, but we're not going to use that as an excuse. We still had a chance to win the hockey game."
Lehner's best save came against Brock Boeser at 10:42 of the second period, when he slid across the crease and robbed the Canucks forward with his glove.
"Well, it was a 2-on-1 and they have a lot of good shooters, so I tried to be aggressive," Lehner said. "He got it across. I know you say I can't save backdoor shots, but the big man can move when he wants too."