The home side made a dream start on 11 minutes when they were awarded a penalty after Yannick Bolasie was upended by defender Ryan Bennett. John O'Flynn made no mistake from the spot and blasted his penalty high into the net past goalkeeper Nick Colgan.
The Bees doubled their lead in the 16th minute when Albert Adomah hit a fantastic low drive into the bottom right corner from 25 yards out.
Barnet continued to control the game and Grimsby never looked like making the breakthrough they needed thanks to centre-half Gary Breen
The scoring was completed in the 67th minutes when Bolasie found himself in space 30 yards from goal and unleashed a ferocious shot into the top corner of the net.
The visitor's misery was compounded in the 87th minute when substitute Micheal Leary saw red for violent conduct after lashing-out at Bees left-back Kenny Gillet.