Exeter completely dominated the first half and had several chances to go in front. Matt Oakley missed at least three decent opportunities while John O'Flynn had a header disallowed after straying offside.
Alan Gow's shot was deflected behind after 34 minutes and from the resulting corner, Gow supplied the ball for captain Danny Coles to power a header into the net from six yards.
Exeter doubled their lead on the stroke of half-time when another Gow corner was headed goalwards by Coles but hit an Exeter player, with Scot Bennett reacting quickest to poke the ball home from eight yards.
Exeter continued to dominate after the break but Barnet played considerably better.
An injury to Edgar Davids, who assumed sole charge of the Bees on Friday after Mark Robson's departure, saw him limp off midway through the second half.
And it was his replacement, Jon Nurse, who gave Barnet a lifeline with a shot across goal that went in off the far post in the 76th minute.
Barnet saw plenty of possession and then deep into stoppage time Exeter failed to deal with a long ball pumped into their penalty area and Iro bundled home from close range.