The Scot's 12th minute goal gave Wednesday the edge going into Monday's second leg at Griffin Park but Paul Sturrock's side will rue their inability to turn possession into goals.
Both sides started slowly and it took 11 minutes before the first chance of the game was created. James Quinn capitalised on Kevin O'Connor's weak back-pass but Stuart Nelson was out quickly to thwart him.
However, just 60 seconds later Wednesday broke the deadlock to the delight of the their 27,000 fans.
McGovern's cross found Lee Peacock who headed back across goal. Quinn swivelled on the penalty spot and back-heeled to McGovern who rifled the ball home from 16 yards, past the despairing boot of Sam Sodje on the goal-line.
McGovern came within a lick of paint of doubling the host's lead in the 22nd minute when his volley, from Matthew Hamshaw's cross, slammed against the crossbar.
Wedensday were on top and went close again when Glenn Whelan stung Nelson's fingers with a low free-kick.
Brentford, who had pinched five points from the Owls during the season, did not muster an effort on goal until the 33rd minute when young Darren Pratley tested David Lucas with a low volley.
Stewart Talbot had a volley deflected wide as Brentford began to come out of their defensive shell.
Hamshaw crafted Wednesday's first chance of the second half with a flighted ball over the Brentford defence which Peacock controlled superbly but his effort sailed over the crossbar.
Hamshaw whipped in another cross in the 67th minute that Peacock flicked on and this time it was Quinn whose effort flew over the bar. Brentford pushed forward looking for an equaliser but their defensive display leaves them with it all to do on Monday.