But it was disappointment for new Terriers manager Danny Cowley who, along with his brother and assistant Nicky, suffered defeat in their first outing at the Huddersfield helm.
Both sides created good chances, but it was Fletcher who gave the Owls the lead with his fourth goal in six games.
And striker Winnall came off the bench to score his first goal since December 2017, which came during a loan spell at Derby. It was his first Owls goal since August 2017.
Owls striker Adam Reach shot straight at Grabara in the fifth minute as the visitors started brightly, before Chelsea loanee Trevoh Chalobah forced a smart stop from keeper Keiren Westwood at the other end.
But it was Scotland international Fletcher who gave the visitors the start they craved.
Winger Harris whipped in an inch-perfect cross from the left and Fletcher rose to head home.
Kongolo let rip with a stinging drive 10 minutes before the break but Westwood palmed the ball away.
A loose ball fell fortuitously to Jacob Murphy on the edge of Huddersfield box on the stroke of half-time, but the on-loan Newcastle midfielder blazed high and wide.
Former Manchester United forward Campbell latched on to a cross from Adama Diakhaby, but his goalbound effort lacked any sting.
And it was replacement Bacuna's brilliant work and cross from the byline which set up Kongolo to force a smart one-handed block from Westwood at his near post.
The Owls kept pushing, though, and Reach went close with a left-foot shot which just whistled past the right upright and also rifled a left-foot shot straight at Grabara.
Winnall then settled the game with 18 minutes remaining as he glanced in a header from skipper Barry Bannan's delightful cross.
Reach had a shot deflected wide as the Owls nearly grabbed a third, but they had already done enough to earn their first points in three league outings.