Connor McDavid scored 52 seconds into the game to give the Oilers a 1-0 lead, tipping in a point shot from defenseman Matt Benning.
Golden Knights center William Karlsson scored at 12:57 to tie it 1-1, redirecting defenseman Shea Theodore's point shot over Talbot's shoulder.
Oilers forward Alex Chiasson scored on the power play at 16:33 of the first period when he lifted a rebound over Fleury to give Edmonton a 2-1 lead.
"We weren't very happy with our first period and then we made some really good adjustments inside the dressing room with players taking control of the situation and making sure everybody was contributing," Golden Knights assistant coach Ryan McGill said. "I think in the last 40 minutes, everybody did contribute."
The Golden Knights tied it when forward Cody Eakin scored shorthanded at 2:21 of the second period. Eakin collected a loose puck at center ice, skated into the Oilers zone and snapped a shot over Talbot's blocker.
"There was a turnover and then a bad pass and I was able to get the puck and it was a 2-on-1 and I shot through a screen," Eakin said. "It was a good way to tie it up. We came out strong in the second, one thing led to another and we had a few in the back of the net. That's what we needed."
Golden Knights forward Max Pacioretty made it 3-2 at 3:53 when his centering pass banked in off Benning's skate.
Marchessault extended the lead to 4-2 with a power-play goal at 4:33. He scored again 34 seconds into the third period off a pass from Miller.
"We did a lot wrong," Oilers coach Todd McLellan said of Eakin's shorthanded goal. "We were sloppy breaking out, we fell behind the net, we turned it over from there, put it in the feet of one of our players, didn't challenge the rush and didn't get the save, so that's five mistakes in about 10 seconds of play.
"Unacceptable. That changed the momentum and I think triggered a five or six-shot barrage where four of them went in, and it's tough to recover from that."
Smith gave the Golden Knights a 6-2 lead at 3:04 of the third before Draisaitl scored at 3:44 for the 6-3 final score.
Golden Knights defenseman Nate Schmidt returned from a 20-game suspension for violating the NHL/NHLPA Performance Enhancing Substances Program and was plus-1 in 19:38 of ice time.
"It was just fun to be back," Schmidt said. "I thought we skated really well in this game and I haven't been here in the last little while, but I felt like our room was good between periods."
