The Bees opened encouragingly at Edgeley Park and were only denied by the woodwork after just six minutes. Glenn Poole picked up a loose ball and smashed a thumping low shot from 25 yards against the base of a Stockport post.
Striker Alan Connell blasted well over for the visitors, then on 16 minutes he planted a free header wide from Gary Smith's corner-kick.
Stockport's first chance came in the 22nd minute. Ryan Lowe crossed for Leon McSweeney, but his half-volley from close range was deflected just over the crossbar.
On the half-hour mark Brentford had a chance to break the deadlock when they won a free-kick just outside the Stockport box, but skipper Kevin O'Connor fired his effort straight at 'keeper Conrad Logan.
At the other end McSweeney found acres of space down the left, but disappointed his unmarked team-mates when he fired straight at 'keeper Ben Hamer.
The hosts went in front just three minutes after the restart with a dream debut goal from 19-year-old full-back Havern. He latched on to a Michael Rose long throw-in before firing low into the corner from 18 yards.
Connell responded for the Bees when he saw a decent shot saved by Logan, then Poole curled a shot narrowly over from 20 yards.
At the other end another Stockport debutant, sub Amari Morgan-Smith, forced a fine save out of Hamer following an impressive run down the right.