J.T. Miller had a goal and an assist, and Brock Boeser and Tyler Myers scored for the Canucks (2-2-0), who have lost two straight. Elias Pettersson had two assists, and Thatcher Demko made 32 saves.
"Loved the battle, hats off to the guys because they competed," Vancouver coach Rick Tocchet said. "We've just got to clean up the crucial mistakes. ... For the overall team effort, the guys played hard until the end."
Paul gave the Lightning a 1-0 lead at 11:10 of the first period with a power-play goal when he stuffed in a rebound off a shot from Stamkos.
"There's some good players out there making some good plays," Paul said. "Right now [the power play] seems to be clicking. We just have to stay consistent."
Boeser tied it 14 seconds into the second period 1-1 with a one-timer from the slot off a pass from Miller, and Myers put the Canucks ahead 2-1 at 1:02 with a slap shot from the high slot.
“I thought we played a much better game than our last game," Boeser said. "We were pretty good until we let a few in late in the second there. Small letdowns you can't have. ... Little details we've got to clean up."