Stars rookie goalie Mike Smith had a shutout going until Manny Malhotra tied it 1-1 with a slapshot from the left circle with 6:57 remaining in regulation.
Nash stepped off the right half boards, fended off defenceman Mattias Norstrom and beat Smith from the slot for his 26th goal.
Stu Barnes scored for the Stars, who have lost two straight but are 10-3-1 in their last 14.