With the scored tied 1-1 late in the first period, New York's John Tavares broke in on net, forcing a commitment from Oilers goalie Devan Dubnyk. But he instead found Moulson alone in the crease with a behind-the-back pass, who buried it into an empty net and put the Islanders ahead for good.
Tavares and P.A. Parenteau each picked up a score and assist each while Matt Martin also found the net for New York.
Islanders goalie Evgeni Nabokov earned the win, stopping 28-of-29 shots.
Dubnyk finished with 25 saves and Sam Gagner scored as Edmonton dropped its ninth in 12 games.