Theodore picked the top corner off a feed from Jonathan Marchessault, who scored the tying goal with eight minutes left in the third period.
''It was a gutsy effort, three in four nights, playing last night and then back-to-back,'' Vegas coach Peter DeBoer said. ''I thought our guys showed up and really did a good job, every guy out there that dressed, goalie on out.
''It was a big win for us, especially a big team win.''
Nicolas Roy also scored for the Golden Knights (39-24-8), who improved to 11-2-0 in their past 13 games. They are three points up on Edmonton for the division lead.
''It's huge. We're getting down to crunch time here and everyone is jockeying for positions and playoffs and the standings,'' Vegas defenseman Alec Martinez said. ''We knew this was going to be a big trip for us, and obviously we weren't too happy with the start of it, but between last night and tonight we're happy to get the win.''
Alex Chiasson and Ryan Nugent-Hopkins had the goals for the Oilers (37-24-9), who played without captain Connor McDavid due to an illness.
Vegas finished with a 48-24 advantage in shots on goal.
''We are just playing a real disconnected game,'' Edmonton coach Dave Tippett said. ''We are just not playing very well as a group right now. I thought we had addressed some things this morning, but our execution is so poor in a lot of different situations.
''We can't continue to play like that and feel like we are a good team.''
Edmonton got the scoring started nine minutes in as Chiasson tipped Oscar Klefbom's shot past goalie Marc-Andre Fleury for his 11th of the season and third in four games.
Vegas drew even with a power-play goal with three minutes remaining in the opening period. Nate Schmidt's point shot was deflected by Roy before it clipped off Edmonton goalie Mikko Koskinen's glove and in.
The Golden Knights outshot the Oilers 15-3 in the first period.
There was no scoring in the second - the best chance being a crossbar hit by Vegas forward Nick Cousins - and the shots were at 30-14 after 40 minutes.
The Oilers regained the lead seven minutes into the third when Kailer Yamamoto battled hard to send the puck in front, allowing Nugent-Hopkins to score his 22nd.
Marchessault tied the game with his 22nd goal and first at even strength in 18 games.
NOTES: It was the third of four meetings between the teams this season. They split the first two, both played in Vegas. Their final matchup is March 31 in Edmonton. ... In addition to McDavid, the Oilers were without Joakim Nygard (hand) and Mike Green (knee). ... Out with injuries for the Golden Knights were Alex Tuch (leg) and Mark Stone (lower body).
Golden Knights: Play the fourth game of a five-game trip in Minnesota on Thursday.
Oilers: Continue their homestand against Winnipeg on Wednesday.
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