Barnet started the better of the two sides, Coulthirst having a shot on target saved after just 24 seconds.
Watson volleyed wide of target from Nicholls knock down before McNulty was denied by Legg.
Coulthirst was then sent through on goal by Akinde but the Bees’ top goal scorer was denied by Burge.
Further chances for Watson and Weston came and went before Burge produced a spectacular save to deny Coulthirst’s right footed curling effort.
Barnet started the second half much like they did the first, Watson forced Burge into a save after just 13 seconds
Vilhete fires wide prior to a good delivery from Alex Nicholls on the left wing which nobody in Amber got on the end of.
Coventry started to pressurise George Legg’s goal from the hour mark. Barrett had an effort headed away by Santos before McNulty headed down into the ground and the ball looped narrowly over.
The hosts took the lead in the 75th minute when Jonson Clarke-Harris yapped home at the far post after getting on the end of a very good, low cross.
The Bees failed to create any further clear cut opportunities as Coventry defended resolutely.
Attendance – 7,127 (353 Barnet)
Barnet – Legg, Santos, Watson, Weston (c), Akinde (Akinola ‘78), Coulthirst (J. Taylor ‘78), Tutonda, Bover (Nicholson ‘78), Vilhete, Nicholls, Sweeney.
Unused – Ross, Clough, Plavotic, Briggs