The visitors, looking to end a four-game losing streak, made a dream start when Danny Graham headed them in front inside five minutes.
But Leven struck five minutes before half-time and Spanish centre-half Miguel Llera nodded home the second, with Leven's penalty sealing the points in the last minute.
It extends the Cumbrians' abysmal losing streak to five and pushes the Dons into the play-off places.
Perhaps it was the early kick-off but MK Dons started the game as if they were half asleep and Graham but the visitors ahead after just four minutes.
On-loan Sunderland midfielder Graham Kavanagh was given too much time. His shot from the edge of the box was punched clear by Willy Gueret but Kavanagh latched on to his own rebound and got the ball out wide for Cleveland Taylor.
The United winger was also given too much time as he picked out Graham who headed superbly past the helpless Gueret.
With confidence high after taking the lead, Carlisle almost made it 2-0 when Marc Bridge-Wilkinson tried to play through Graham. The ball cannoned off Llera's shins and back to the midfielder but he shot straight at Gueret's legs.
As the half went on, the Dons did start to get into the game. Llera had a header cleared off the line by Taylor from Leven's cross while Sam Baldock skimmed the bar from Mark Wright's cross.
A goal looked like it was coming and it eventually did in the 38th minute. Another Wright cross wasn't properly cleared by Danny Livesey and the ball fell invitingly to Leven on the edge of the box and he hit a lovely right-footed shot into the bottom corner of the net.
There was only ever going to be one winner in the second half as MK Dons took control against the deflated visitors.
The second goal came just after the hour mark when Leven's wicked cross found Llera at the back post and he nodded home.
The Dons continued to press and Shaun Cummings could have wrapped up the win only to curl his shot over the bar from the edge of the box.
But it didn't matter as, in the closing stages, substitute Jude Stirling twisted and turned Livesey before being brought down inside the area.
Leven stepped up and blasted his penalty straight down the middle to cap a virtuoso performance from the Scotsman.