"He's a gifted, gifted player," Lightning coach Jon Cooper said. "You get him that close to the net with the puck, a little bit of time and space, he can do some pretty magical things."
WATCH: All Lightning vs. Avalanche highlights
The Lightning (26-24-8) are five points behind the Toronto Maple Leafs for the second wild card into the Stanley Cup Playoffs from the Eastern Conference. They are 4-0-2 in their past six games and 3-0-3 in their past six on the road.
"I was gassed," Drouin said. "Keep the puck, get it off, get it off. I made a move and sent it through. It's one move, go one way and hopefully [Pickard] bites on that move, and I think he did a bit."
The Avalanche (16-38-3) got third-period goals from Mikko Rantanen at 2:46 and Matt Duchene with 41.9 seconds remaining after Pickard went to the bench for a sixth skater.
The Lightning also squandered a 2-0 lead Saturday in a 4-3 overtime loss to the Dallas Stars.
"We needed that [extra] point, definitely [after] blowing that two-goal lead in the third period as well," Drouin said. "We made sure we got that point and leave here off a back-to-back with three points."
Ben Bishop made 27 saves for Tampa Bay but had little chance to prevent Duchene's tying goal. Duchene, who had gone 13 games without a goal, scored his 16th of the season with a shot from the right circle that caromed into the net off Lightning defensemen Victor Hedman and Jack Dotchin.