Marcelo Bielsa's side were roared on by a 7,717-strong following, but Danny Graham's towering header gave the hosts into a second-minute lead.
Only fine goalkeeping kept Leeds in the game, before Mateusz Klich equalised from close range on the stroke of half-time - his fifth goal this term.
Despite dominating possession for large spells, Lenihan's first of the season 20 minutes from time handed Leeds a first away defeat of the season.
It was rich reward for the hosts, who moved fifth after an energetic and clinical display that gave them back-to-back league victories for the first time this season.
Blackburn made four changes from their victory at Bolton, while Leeds were without the suspended Luke Ayling but were able to call upon fit-again duo Kemar Roofe and Gaetano Berardi.
Rovers charged out of the blocks and took an early lead when Graham met Harrison Reed's corner to send a thumping header into the top corner for his fourth goal of the campaign.
Leeds settled into their high intensity game and Samuel Saiz stung David Raya's palms in the 11th minute, with Pontus Jansson directing a free header over the crossbar from the resulting corner.
But Rovers were the more dangerous of the two sides and only a sensational Bailey Peacock-Farrell save kept the deficit at one when Blackburn's leading scorer Bradley Dack weaved around a challenge and into the area.
Adam Armstrong went even closer just before the break when he collected Elliott Bennett's sumptuous cross-field pass and engineered space, only to curl his effort agonisingly onto the roof of the net.
An outstanding team move levelled matters in first-half stoppage time as Saiz's diagonal ball found Berardi, who beat the offside trap.
He squared to the unmarked Klich and he hammered the ball into the bottom corner from six yards.
Gaetano's weak header back to his goalkeeper almost cost Leeds dearly in the 55th minute but Peacock-Farrell was alert and out quickly to smother Armstrong's effort.
Yet despite Leeds' overall dominance of possession, it was Blackburn who went back ahead when Lenihan rose highest to meet a corner, heading into the bottom-right corner and past the despairing dive of Peacock-Farrell.
The visitors pressed for an equaliser but once again needed Peacock-Farrell to keep them in with a chance as his outstretched foot diverted Armstrong's low drive away.
At the other end, Klich thought he had equalised with a curling 25-yard shot but Raya produced an acrobatic save to tip over, and although the visitors thought they should have had a late penalty, nothing was given and Rovers hung on for a well-earned win.
United, who lost at Blackburn for the first time since November 2014, have now won only one of their last five games.
Bielsa said: "We needed to win this game, especially after the draw in the last home game.
"We didn't defend as well as we used to do. The offensive players created difficulties for our defence. We could have avoided the goals they scored. Our offensive play was good enough.
"Klich and (Samuel) Saiz had an offensive and positive influence.
"What we can say is that we lost against a rival that is not better than us. Maybe a draw would have better reflected what happened in the game. We played better when Blackburn were winning, and this is a defect.
"The negative results are always a source of worry. I also evaluate the play but the feeling I have for the game of today are better than the recent ones.
"Our offensive play against Brentford was not as good as it was today. I'm talking about the number of chances we had, but how we built the offensive play.
"But with the last draw and today's loss, we have to conclude we're in a bad moment."
After ending a run of three games without a win at home, Mowbray talked about the importance of preparation, and how his team made that count to hurt Leeds.
He said: "We'd had an international break to prepare. It gives the staff a good chance to study the opposition when you've got two weeks to watch five or six full games, try to pick their weaknesses and strengths.
"You come up with gameplans and we had two days to put it together. I'm just so pleased for the players really. The set-plays today are something we worked really hard on.
"Pontus Jansson is a monster of a man and (Liam) Cooper is dominant but you take those two out of the box, we felt they were vulnerable, which is what happened.
"Whoever was getting marked by those two played wide; for the first goal Graham came powering through the middle and scored. For the second goal, Lenihan did the same.
"But we had to dig in. They're a great team, with wonderful footballers and a world-class coach who has got them playing attractive football. It doesn't mean you should succumb. You have to fight, stand up and be counted. We did that today."