Dallas won its third straight and improved to 3-1 on a five-game road trip that has taken the Stars from coast to coast. The journey ends Friday with a game against New Jersey.
Kyle Okposo put the Islanders in front with 1:36 to play in the second period, but Dallas jumped on goaltender Kevin Poulin early in the final stanza.
Morrow scored on the power play 67 seconds into the third and Benn produced his ninth goal of the season 4:33 into the session.
The Islanders lost their fourth straight and remained stuck on nine wins for the season, tied for fewest in the NHL.
Rookie goaltender Richard Bachman, called up this month when starter Kari Lehtonen was injured, improved his career record to 3-0 with 25 saves. He has given up three goals in his three starts.
Poulin stopped 26 shots.