It was a poor start for the home side when after just five minutes Jake Hyde bundled the ball home for Barnet.
But Fleetwood were handed a way back into the match after 24 minutes when Stack upended David Ball and referee Richard Clarke showed the shot-stopper a straight red, with Ball himself converting the penalty.
Jamie McGuire nearly gave Fleetwood the lead on the hour mark, his header superbly kept out by substitute keeper Sam Cowler.
But it was only a matter of time before the home side got their second and it came with 10 minutes remaining - Junior Brown's cross finding on-loan Blackpool midfielder Tom Barkhuizen whose header squirmed past Cowler into the goal.
There was a late scare for Fleetwood when Ricky Holmes' long throw caused confusion in the box but in the chaos the Bees were unable to find the target. Jamie Milligan's late free-kick almost added a third for Town, rattling the woodwork but not crossing the line.