The Flames, who are 16-5-1 in their past 22 games, trail the Sharks by three points.
"The whole West, all in all, you can pick anyone any given night," Versteeg said. "That's what's exciting about it."
Shaw scored the game-winner on Kesler's rebound with 3:06 remaining to give the Ducks a 4-3 lead.
"It's playoff hockey and you want to throw pucks to the net and make their defensemen turn," Shaw said. "When I saw [Kesler] going, I figured I may as well jump up there with him. I knew he was going to throw the puck at the net or behind the net, so I was just going to the right place."
Eaves scored his seventh goal in the past eight games and 30th goal of the season on the power play at 11:32 of the first period to give the Ducks a 1-0 lead, and Silfverberg scored at 19:03 when he took a drop pass from Kesler and shot by Elliott's blocker to make it 2-0.
Versteeg tied the game with consecutive power play goals in the second period. He scored 3:48 into the period, and again at 10:01 on a 5-on-3 man-advantage.
Holzer gave the Ducks a 3-2 lead at 17:53 of the second period, and Frolik tied the game 3-3 at 5:42 of the third when he redirected Mark Giordano's point shot.