Namestnikov gave the Lightning a 3-2 lead at 8:09 of the second period when he scored on a rebound of a shot by Tyler Johnson.
Budaj made 28 saves, including stopping Avalanche forward J.T. Compher on a breakaway in the second period that would have tied the game 3-3.
"I think the puck was bouncing a little so he didn't get a good shot off," Budaj said. "And [Victor Hedman] was right on him, so that made my job a little easier."
Killorn scored a power-play goal at 4:57 of the third period to give Tampa Bay a 4-2 lead, and Point scored a shorthanded empty-net goal to make it 5-2 at 16:41.
"We had a really, really strong first, it's too bad we couldn't come out with the lead, but we knew we were playing well," Lightning coach Jon Cooper said. "And the power play scored again and it was a big goal for us."