Goals from Devante Rodney, James Ferry and former Bee Manny Duku secured a comfortable win for FC Halifax Town over Barnet.
Cousins was the first keeper to be tested in the 17th minute when Quigley got into a shooting position, looked to round the Barnet number one but Cousins stood firm to make a good save.
A good chance for Duckworth followed but his effort from 35-yards out went just over the bar before, at the other end, Alexander's cross towards Coulthirst was turned behind.
Halifax kept piling on the pressure when captain Reynolds did well to head Sellers' free kick away from underneath the crossbar.
The deadlock was broken in the 36th minute when Cousins pulled off a great save to deny Kosylo but Rodney fired home the rebound.
Barham had his first chance of the game shortly before half time, but his turn and shot, from Johnson's ball, was off target.
After the break, Robson's header from Elito's corner was forced the home keeper into a rare save.
Soon after, Sam Johnson was tested again when Elliott Johnson's low cross was played in towards Coulthirst but the Halifax man claimed at the second attempt.
However, Halifax continued to create chances and doubled their lead in the 60th minute, Ferry finishing at Cousins' near post with a low, bobbling effort from 12 yards.
Substitute Manny Duku, who was on-loan at The Hive earlier this season, made it three when he finished off a flowing home attack, made by Rodney.
Barnet were given a chance to pull one back when Coulthirst was fouled in the box. The Bees number 10 stepped up but his spot kick was saved by Johnson.
Substitute Akinola would see a powerful shot deflected over and Coulthirst's header in stoppage time was wide.
Barnet - Cousins, Alexander (Tutonda), Johnson, Reynolds, Robson, Coulthirst, H. Taylor, Fonguck (Akinola), Elito, Sweeney, Barham (Tarpey)
Unused - Matrevics, Mason-Clark
Attendance: 1,085 (57 Barnet)