The Predators completed a perfect three-game road trip, getting a goal from Patric Hornqvist with 6:22 left in the third period.
Ellis has 10 shutouts in three full seasons in the NHL. He got the best of hard-luck loser Miikka Kiprusoff, who stopped 20 shots.
Calgary has lost three in a row and five out of six.
Hornqvist worked a give-and-go with Steve Sullivan for the goal, his 18th of the season.
Nashville's three straight wins have lifted them to 61 points, the third best total in the Western Conference behind San Jose and Chicago.