Bouchard scored with a slap shot from the right point 11 seconds into the second period to cut it to 2-1.
"After the first, we're like, 'You know what, what could possibly go more wrong, so just go out there and start working,' and we did," Oilers defenseman Mattias Ekholm said. "We got a good start, right off the bat, with a big goal, first shift, and just kept on plugging away from there."
Kasperi Kapanen scored his 100th NHL goal with a one-timer from the bottom of the left circle while on a power play to tie it 2-2 at 6:30.
Bouchard scored his NHL-leading sixth goal of the season with a slap shot from above the circles to give the Oilers a 3-2 lead at 14:12.
"We came out flat at the start of the second and we can't do that," Sennecke said.
Draisaitl made a stretch pass to Vasily Podkolzin as he slipped behind the Anaheim defense and he scored on a breakaway to make it 4-2 at 16:49.
McDavid entered the Anaheim zone with speed and slipped the puck between Dostal's pads from above the left hash marks during 4-on-4 play to stretch the lead to 5-2 with 52 seconds left in the period.
"They scored at the beginning of the period and the end of the period in the last minute," Quenneville said. "In between, we didn't do much. I think we watched a lot."