The second period wound up being a shootout.
Pouliot gave Phoenix the lead back by flipping a backhander past Quick on a loose puck in front for his first career playoff goal. Doughty tied it a few minutes later, scoring from just inside the blue line on a shot Smith had trouble seeing through traffic.
Richards scored on rebound to put Los Angeles up 3-2, Yandle tied it again after a pass by Pyatt caromed off his right leg past Quick.
Both teams had numerous scoring chances in a hectic third period, but both goalies made some superb saves.
They went back and forth in the overtime, too, until Penner finally ended it when a shot by Jeff Carter caromed out front to him in the slot.
"It's the biggest goal of my career so far," Penner said. "Hopefully, there are a couple more waiting in the finals."
NOTES: Coyotes RW Radim Vrbata had an assist on Pyatt's goal for his first point in eight games. ... Los Angeles was 2 for 27 in the series on the power play after going 0 for 4 in Game 5. ... Yandle had nine points in the playoffs, matching Dave Babych's team record for a defenseman set in 1985. ... The Kings are the seventh team to reach the Stanley Cup finals in 14 games (12-2) since the NHL went to a four-round best-of-seven series format in 1987.