Ok, I was annoyed at this, so I pulled out the movie and watched the scene.
It would appear, and from what I remember from my aerodynamics class, that he increases thrust, and also angle of attack (ie he pulls up). This would cause the airplane to slow, and if all else is constant, ie Jester doesn't slow down or increase his own thrust, the the F14 should climb above, but due to the increased drag on the plane also slow. As Jester's plane is now faster it would "shoot" in front of Mavericks plane, all he has to do now is nose over and follow.
However what doesn't make much sense to me, even a rookie pilot could tell when a plane is climbing, and Jester should have been able to compensate for it, especially as, "the planes you'll be flying against are faster, smaller, and more maneuverable, just like the enemies."
I think I got this right, i don't want to drag out the Aerodynamics book.......
Side note, what is the airplane they are flying against in Fighter Weapons School? I cant remember it...