Price was in goal for each win and made 43 saves in Calgary after not starting for a week; he backed up Antti Niemi for two games after going 1-3-1 with an .854 save percentage in his previous five starts.
"We know how calm he is, how ready he is every game," Drouin said. "Last few games, we saw the Carey Price where pucks just hit him and he's never out of position."
Elias Pettersson and Del Zotto scored and Markstrom made 28 saves for the Canucks (10-10-2), who have lost five straight games (0-4-1).
"For me to let in two in the last 10 minutes of the third, it's very frustrating," Markstrom said. "I don't care how it looks, but we've got to win, especially those tight games."
Tatar scored on a breakaway at 8:07 of the second period to make it 1-0, finishing a nice stretch pass from defenseman Jeff Petry with a wrist shot over Markstrom's glove.
It was the sixth goal in the past six games for Tatar, who was acquired in the trade that sent forward Max Pacioretty to the Vegas Golden Knights on Sept. 10.
Del Zotto scored his first of the season to tie it 1-1 at 16:13 of the second period when a point shot deflected in the slot right to him at the side of the net.
Pettersson scored his team- and NHL rookie-leading 11th goal on a power play one-timer to put the Canucks ahead 2-1 at 10:09 of the third period. It was Pettersson's 11th goal of the season and first point in five games.
"I've had some games where I haven't created that much. It was a little relief to finally get one," Pettersson said. "We've just got to find a way to win. We've just got to face the reality and be better. We can't hide from it. We've just got to be better."
Shaw tied it when Max Domi's centering pass deflected in off his skate at the top of the crease.
"It brings back some of that Calgary game a little bit, where you are down a goal on the road and you have to show character, you've got to find a way to put the puck in," Drouin said. "If you look at our tying goals, they're not pretty; they're just around the net and that's something we can build on."