The Bees, who were a goal down after 33 seconds against Preston North End last weekend, were nearly behind again early on after Tom Lees found space to shoot on the edge of the box, but failed to test David Button.
Wednesday, fresh from beating Premier League Newcastle United in the Capital One Cup, continued their bright start at Griffin Park and almost found a breakthrough when Daniel Pudil swung in a menacing cross, only for his delivery to evade the head of Nuhiu.
On nine minutes, Nuhiu managed to meet another cross, but the forward failed to make a firm connection as Button was able to gather comfortably.
The Owls had another chance soon after as Ross Wallace's drive stung the palms of Button, but Wednesday failed to convert their early opportunities.
Midway through the half, the visitors were denied by the woodwork as Nuhiu headed Wallace's cross against the crossbar.
Soon after, Wednesday were again on the attack as Marco Matias's fizzing drive was met by another save from Button.
Brentford's best opportunity of the opening half-hour came when Marco Djuricin took aim at the visitors' goal before he was closed down by the Owls defence.
The Bees went closer still after Jake Bidwell sent a looping effort on the bar as the hosts looked to settling into the game in the latter stages of the half.
However, Wednesday were awarded a penalty before the interval when Nuhiu broke clear of the Brentford backline, but was brought down by James Tarkowski.
After deliberations between the officials, Tarkowski was given his marching orders before Nuhiu slotted his spot kick past a helpless Button.