The hosts took the lead midway through the first half after Sam Hutchinson gave away a needless penalty, hauling back Lewis Macleod as he tried to run onto a throw in.
Bees’ top scorer Maupay thumped his third of the season past Cameron Dawson to give Brentford the start they wanted.
The Bees stretched their advantage just after the hour mark, Maupay racing clear from his own half before drawing the goalkeeper and squaring for Watkins to stroke home from 12 yards.
It was all Brentford in the opening half, but the final ball lacked the quality to unlock a resolute Wednesday back four.
Watkins was a constant threat on both flanks and forced a save from Dawson after cutting in from the left to fire in a rasping low drive that the goalkeeper stopped at the second attempt.
Sergi Canos burst clear just before the half-hour mark and cut in from the left, but his 20-yard strike was saved by Dawson.
The Owls’ first effort of a one-sided first half came when Barry Bannan raced onto a loose ball, but he blazed high and wide.
Just before the break Wednesday striker Marco Matias raced onto a Bannan through ball, but fired his shot straight at the onrushing Daniel Bentley.
Then at the other end Canos was equally guilty of wasteful finishing.
After the break the Bees could have run in six or seven against the hapless Owls.
Canos was guilty of a handful of misses or denied by Dawson and Watkins, played in by Maupay, was thwarted at close range.
Watkins should have made it three after 74 minutes when he charged in from the left, but curled past the far post instead of squaring for substitute Said Benrahma, arriving fast at the back post
Brentford resisted Wednesday’s physical approach, which almost reaped rewards when Matias hooked a rare effort just over the bar late on, but that was all they really had to offer all afternoon.
Brentford: Bentley, Dalsgaard, Konsa, Mepham, Barbet, Macleod (Mokotjo 71), McEachran, Sawyers, Canos (Benrahma 72), Maupay, Watkins (Judge 77). Unused substitutes: Yennaris, Woods, Jeanvier, Daniels.
Sheffield Wednesday: Dawson, Baker, Lees, Pudil (Penney 84), Thorniley, Hutchinson (Preston 46), Bannan, Pelupessy, Marco Matias (Fletcher 76), Nuhiu, Forestieri. Unused substitutes: Palmer, Wildsmith, Kirby, Jack Lee.
Referee: David Webb (County Durham).