The Bees were always on top against the play-off hopefuls and Byrne reacted fastest to open the scoring at Underhill on Tuesday night before Gambin made sure of the points after a terrible defensive mix-up.
The win moves Edgar Davids' side two points clear of the relegation zone, and it was skipper Byrne who showed the way for the hosts.
Curtis Weston's close-range shot was blocked by Scott Davies in the Fleetwood goal but Irish midfielder Byrne was on hand to fire home in the 23rd minute.
Alan Goodall came close for the visitors before the break but it was Barnet who always looked the more likely to add to the scoresheet.
And after the break it was Gambin who struck, walking the ball into an empty net after a terrible miscommunication between Davies and Shaun Beeley left the keeper stranded.
Late on, Jon Nurse had a chance to seal it for the Bees but fired wastefully wide, before Byrne was denied.