Ellis stopped 23 shots and recorded his 11th career shutout as the Lightning beat the Phoenix Coyotes 3-0 on Saturday night.
Ellis, who signed as a free agent after three seasons with Nashville, was helped by a defense that limited the Coyotes to few scoring chances.
"We frustrated their zone entry and that was the key to the win," Ellis said. "Our defense pushed play to the outside and I was able to see shots. We have a great system, executed it to a T, and that equaled success."
Ellis' last shutout was on Jan. 15, when he blanked the Flames in Calgary for Nashville.
The Lightning's first goal was from newly acquired Mattias Ritola. It took nearly two periods, but the Lightning scored when Ritola, picked up from Detroit on Oct. 6, scored his first NHL goal on a wraparound to the right side of the Phoenix net.
Nate Thompson's pass off the right wing board was deflected off Phoenix defenseman David Schlemko's skate and in behind Bryzgalov. Adam Hall was credited with his second goal of the season at 4:26 of the third period.
"Phoenix is really a good skating team with speed," Hall said. "We were able to cut their chances. Anytime you can get two points on the road, that's a great accomplishment."
Stamkos scored his ninth goal of the season on a backhander with 5:22 left to play.
If the Lightning entered the game as one of the highest scoring teams in the league, their defense was equal. Phoenix was limited to 13 shots through the second period, and the Coyotes had few good scoring chances against Ellis, making his sixth start of the season.
Through a scoreless first period, the Lightning had the better opportunities and they came in a quick secession of shots, both off the stick of Steve Downie less than 5 minutes into the game.
Crashing the net down the right wing, Downie's shot, headed high and under the cross bar, was stopped when Bryzgalov slid across the crease for the save. Seconds later, Downie cranked a slap shot off the left post.
The loss drops the Coyotes to 3-4-3, but there are no signs of panic.
"Obviously, we're not 10-0, so we have a great deal of work to do," defenseman Keith Yandle said. "The good thing being 10 games in is we have 72 games left where we can get better."
The crowd was announced at 8,171, the third straight below 8,200. Lightning began a four-game West Coast trip and a stretch of nine of their 11 games on the road. Martin St. Louis appeared in his 400th consecutive game for Tampa Bay. Pavel Kubina is one goal short of tying Tampa Bay's franchise record for most goals by a defenseman. ... Coyotes F Martin Hanzal missed his sixth straight game (lower back).