Kiprusoff made 14 saves and Anton Babchuk scored on the power play for the Flames, who scored three goals during their three-game skid.
“Obviously, this is something we can build on,” Calgary coach Brent Sutter said. “To come into this building and play as well as we did, it’s a plus.”
Ribeiro scored a power-play goal and Lehtonen stopped 31 shots for the Stars, 10-0-3 in their last 13 at home.
Dallas heads into a two-day holiday break with 46 points, tied with Detroit for the top spot in the Western Conference.