Benn beat Flames goalie Miikka Kiprusoff to the stick side on the first try of the tiebreaker, and after Stars goalie Kari Lehtonen made a stop on Olli Jokinen, Eriksson trickled the puck between Kiprusoff's pads.
Lehtonen then secured the win with a sprawling toe save on Alex Tanguay, allowing Dallas to leapfrog San Jose into the seventh playoff seed in the West and tie Phoenix atop the Pacific Division with 75 points.
Eriksson added a goal and an assist, and Michael Ryder also scored as the Stars won for the sixth time in seven games.
Lehtonen earned the victory with 36 saves and added an assist for Dallas.
Fading Calgary dropped its sixth in seven games despite tallies from Curtis Glencross and Jarome Iginla.
Kiprusoff yielded two goals on 40 shots.
Notable deaths of 2014 [PHOTOS]