Jamie Benn scored the deciding goal in the 2, on Sunday at Scotiabank Saddledome.
Benn picked up the puck and swung way out wide to the right. He cut across the goal mouth and beat Flames' netminder Miikka Kiprusoff to the stick side.
Eriksson added a goal and an assist in regulation, while Michael Ryder also scored for the Stars, who have won six of their last seven games. Lehtonen made 36 saves and contributed an assist in the victory.
Curtis Glencross and Jarome Iginla scored for the Flames, who have lost six of seven. Kiprusoff gave up two goals on 40 shots in defeat.