Chris Wood scored the only goal of the game, poking in his 23rd of the season from close-range following a misjudgement from Vincent Sasso, while Rob Green saved a Jordan Rhodes penalty.
The win moves Leeds further into the play-off pack, leaving a three-point gap between them and the Owls, who, apart from the penalty, were unable to seriously trouble Green in a hard-fought encounter.
Following the win, which saw his side complete the double over Wednesday this campaign, Monk felt Leeds were deserving victors.
"We were playing a very good side in Sheffield Wednesday," he said. "I thought they put some pressure on but we dealt with it extremely well.
"I can't remember them having any shots on goal apart from the penalty so that was very pleasing.
"The pressure that's there to win these types of games, both teams on the same points, a derby game. I thought we handled the pressure really well today and I'm very pleased with the players."
The decision to award Sheffield Wednesday a penalty 10 minutes into the second half was a contentious one, with Leeds upset they had not been given one moments earlier.
Sam Hutchinson slid in on Eunan O'Kane in the corner of the area only for the referee to wave play on, before penalising Souleymane Doukara for tugging Hutchinson down at the other end.
Green stepped up to produce a stunning save low to his left and tip the ball onto the post to deny Rhodes, who was largely anonymous as his struggles continue following his big-money move.
Monk admitted he would have felt hard done by had the spot-kick gone in.
"I haven't seen them back," he said.
"But at the time we felt a bit aggrieved that we didn't get ours.
"It looked a penalty to me but to go up the other end and have a soft one given against us; you feel a bit aggrieved.
"But (it was) a fantastic save from Greeny - the one time he was called into action - and it was a fantastic save.
"It was reward for the way we defended.
"We played good football and overall, we deserved that win. We were the most creative team on the pitch and deserved the three points."