Theodore, who had zero points in the series ahead of his goal, got one past Utah goalie Karel Vejmelka after he lost his stick.
Jack Eichel finished with three assists on the night.
Vegas is now 7-7 in overtime as the road team in the playoffs (12-14 all-time).
They had thought they originally scored the game-winner, but it was called back after being offside.
Game 5 will head back to Vegas on April 29th, as they also join the Minnesota Wild-Dallas Stars and Montreal Canadiens-Tampa Bay Lightning as the only series these playoffs to reach 2-2 after four games.
Recap & Highlights
The first period was all Vegas. They scored twice, held Utah to just three shots, and killed both of their power plays.
Pavel Dorofeyev scored his first goal of the playoffs to put the Golden Knights up 1-0 just 1:12 into the game. Ivan Barbashev (2) and Jack Eichel (3) picked up the assists.
Heading into this game, Vegas was 42-15 in the playoffs after scoring the opening goal, making their .737 win percentage the fourth-highest in the NHL.
Utah's Michael Carcone had a chance following Vegas' goal to make it 1-1, but he missed a wide-open net.
It would've not only been his first goal of the playoffs, but the first playoff point of his entire career.
That mistake proved costly.
On Utah's second power play of the first, they would get caught sleeping as Vegas doubled their lead.
Brett Howden scored the short-handed goal for his first of the playoffs to make it 2-0 with under two minutes left in the first. Mitch Marner picked up his third assist of the series.
Howden became the sixth player in Golden Knights history to score a short-handed playoff goal.
Things wouldn't get much better for the Mammoth to start the second.
Cole Smith scored his first career playoff goal off a tip-in only 3:16 into the second as Vegas tripled their lead to 3-0. Noah Hanifin (3) and Colton Sissons (2) earned the assists.
However, it took just 29 measly seconds for the momentum to completely shift in Utah's favor.
Nick Schmaltz and Ian Cole would both score their first goals of the playoffs within 29 seconds of each other to make it a 3-2 game - tying the Tampa Bay Lightning for the fastest goals between two teammates these playoffs.
It would be Schmaltz's first career playoff goal in his 11th NHL season, while it was Cole's fourth in his 16th season.
Utah had a chance to tie things up after they went on the power play for the third time in the game shortly after their two goals, but couldn't get it done.
However, that would change in the third...
To follow suit, Utah would get up on the board to tie the game just 1:12 into the third period.
After missing on an open net during the power play earlier in the game, Carcone wouldn't miss on a second opportunity as he scored his first career playoff goal to make it 3-3.
Mikhail Sergachev (2) and Dylan Guenther (3) picked up the assists.
Utah wouldn't stop their rally, and all it took was a few more minutes before the fans in Salt Lake City could be heard from across the country.
Clayton Keller would score his first of the playoffs off a Schmaltz and another Sergachev assist to make it four straight goals to take their first lead of the game.
Sergachev joined Mikael Granlund, Jake Guentzel, Jackson LaCombe, and Mats Zuccarello as the only other players these playoffs to record three assists in a single game.
But that Utah lead would last all but five minutes.
Howden scored his second goal of the game off a tip-in to tie the game at 4-4 with 9:35 left in the third period.
Eichel and Hanifin both picked up their second assist of the game and their fourth of the series.
The game would remain scoreless for those final nine minutes as it went into overtime, where the Golden Knights would come away with the win.
Vegas outshot Utah 36-31, while the latter outhit the former 55-43.