Stingrays, who had won 11 of their last 13 games at home, are now two points behind Stars with just two conference fixtures left while their rivals still have five to play.
It is a sixth loss to Stars in seven meetings this season – all of them being decided by just the one goal.
Stingrays had captain Jeff Smith ejected on a 5+game misconduct for roughing at 11.44, with Jereme Tendler – the leading short-handed scorer in the league – hitting the bar on the penalty kill.
Brock McPherson grabbed the go-ahead goal for Stars at 36.25 but Jason Silverthorn tied the game for Stingrays with a powerplay marker at 48.21 only for Jack MacLellan to restore the visitors’ lead just 28 seconds later.
Carl Lauzon hit a post for Stingrays, who also pulled goaltender Ben Bowns and called a time-out in an attempt to force overtime which proved in vain.