The French goalkeeper was given a straight red card in the 53rd minute for shoving Milutin Osmajic in the face.
After claiming a cross on the edge of his six-yard box, the 23-year-old squared up to Ben Whiteman having felt he had been nudged in the back.
Osmajic immediately darted towards Meslier where he pushed the shot-stopper, with the ex-Lorient star in turn shoving the striker in the face.
Osmajic then hit the deck in dramatic fashion with referee Josh Smith wasting no time in whipping out the red card for Meslier.
And according to ex-Liverpool midfielder Charlie Adam, Meslier can have no complaints over his dismissal.
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Speaking on commentary for talkSPORT 2, Adam said: "I think it's a red card, it's silly from Meslier."
He added: "When you're trying to get a promotion, or you're away from home, you don't need to lift that crowd.
"They've been there with the Preston players so far, and moments like that, you don't need to be doing something silly.
"And Meslier does something stupid, it's a red card."
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It turned out to be the turning point in the match, as Preston took the lead against the promotion chasers four minutes later.
Leeds did find an equaliser in the 83rd minute through Pascal Struijk's penalty, but the hosts took home all three points when Liam Millar fired home at the death.
The Yorkshire outfit could have cut the gap on second-place Ipswich to four points with a win.
But they could now drop to fourth should Southampton emerge victorious against Swansea.
Speaking after the game, Leeds boss Daniel Farke insisted that Osmajic's theatrics got him sent off.
He remarked: "I think it's quite obvious, it's exactly what the Preston player wanted, he catches the cross, and then there was a foul against Illan.
"And then the second player who has nothing to do with the situation runs over and gives him a hard push and Illan reacts.
"Because of this, he goes down and rolls around and dives, it's nothing to do with fair play, he just wants to provoke a red card."
Farke continued: "It was so obvious that he just wanted to provoke, and to dive around and to roll over the pitch, I hate this behaviour."