Tampa Bay took the lead late in the first on a Corey Perry power play goal and never looked back. The Lightning padded the lead with three second period goals, and Mikhail Sergachev put the game away early in the third.
For Vasilevskiy, the shutout is his first of the season.
These two teams will face on another again in five nights at Ball Arena in Denver.
The Bolts now hit the road for a four-game west coast trip that begins on Saturday afternoon against the Stars.
Scoring Summary
1st Period
TBL 1, COL 0
15:15 Corey Perry (10) - Anthony Cirelli, Alex Killorn - PPG
On the power play, Tampa Bay worked the puck to Corey Perry open in front of the net. With his back turned to goal, Perry spun and avoided Alexandar Georgiev's poke check, before sweeping the puck home on his backhand.
2nd Period
TBL 2, COL 0
8:32 Brandon Hagel (20) - Anthony Cirelli, Alex Killorn
Anthony Cirelli beat two Avalanche skaters to a loose puck in the Colorado zone and dished back to Brandon Hagel at the far post for a goal to double the Lightning's lead.
TBL 3, COL 0
10:29 Brayden Point (32) - Nikita Kucherov, Brandon Hagel - PPG
The Lightning moved to two-for-two on the power play with Brayden Point making it 3-0 midway through the second period. Nikita Kucherov didn't get much on his shot from along the goal line, but the rebound managed to be jammed over the line by Point.
TBL 4, COL 0
18:07 Brandon Hagel (21) - Alex Killorn
After Hagel forced a turnover in the neutral zone, Alex Killorn pounced on the loose puck and came charging through the middle of the ice. Killorn had Bowen Byram on his back but left a drop feed for Hagel that was snapped past Georgiev to cap a dominant second period from Tampa Bay.
3rd Period
TBL 5, COL 0
5:44 Mikhail Sergachev (7) - Brayden Point, Pierre-Edouard Bellemare
Tampa Bay essentially put the game out of reach early in the third when Mikhail Sergachev's shot from the point cleanly got through traffic in front of the net and beat Georgiev.
