The young striker scored with five minutes left, and only five minutes after coming on, to give the hosts a share of the spoils.
Adam Chicksen gave Dons a first half lead but the result left the visitors without a win in their last six games, leaving their play-off hopes in tatters.
Dons could have taken the lead twice midway through the first half when Carlisle were down to 10 men while central defender Danny Livesey was off the field having a head cut treated following a collision with Dean Lewington.
Ryan Lowe dragged his shot wide after finding space inside the area then Chris Lines strode purposefully through the middle before forcing keeper Mark Gillespie to dive full length to push his shot away.
Carlisle again lost Livesey for running repairs as Dons took the lead in the 36th minute when Chicksen cut inside to fire past Gillespie.
But Beck, an 80th minute substitute, forced Dave Symington's left-wing corner home at the far post to equalise for Carlisle.