Zack Kassian tied it 1-1 at 2:32 of the second period on a pass from McDavid from behind the net.
Kempe gave the Kings a 2-1 lead at 9:29 following a turnover just outside the Oilers blue line by defenseman Duncan Keith.
Andreas Athanasiou increased the lead to 3-1 at 13:34. Brett Kulak had his clearing attempt from behind the goal line intercepted by Dustin Brown. He slid the puck over to Athanasiou, who lifted it over Smith.
"I feel like we're sticking to our game," Kempe said. "In the second and third game [6-0 and 8-2 losses] we kind of fell into their trap and let them play their rush game, and that's not how we wanted to play. They're a really good team when it comes to transition and I feel in this game and the one before [4-0 win in Game 4 on Sunday], we took it back to playing our game, being physical and solid in the D-zone and outworking them."
McDavid scored on the power play at 2:50 of the third period to cut it to 3-2 when he picked up a loose puck off a scramble on a face-off and scored on a backhand.
Danault extended the lead to 4-2 on a power play at 11:06, sweeping in a pass from Kempe at the side of the net.
"I think at the beginning of the series, if someone would have said would you take 2-2 and go into overtime for Game 5, we would have taken it, for sure," Danault said. "That's what we said, and we kept that positive vibe. We had a big first shift and then right away in the second shift, 'Juice' [Kempe] capitalized."