Jarvis Williams supplied 16 points and five blocks, while T.J. Sapp added nine points and six boards off the bench for the Racers (23-11), who went 16-1 at home during the regular season en route to making the cut for the CIT for the first time.
Javier Duren donated 18 points, five boards and five assists to lead the Bulldogs (19-14), who suffered a first-round loss in their only other trip to this event back in 2012.
Armani Cotton's layup gave Yale a 28-27 lead just over a minute into the second half, but the Racers answered with a 9-1 run, which Payne capped with a 3-pointer for a 36-29 lead with 16:00 left.
The Bulldogs battled back with six straight points before Payne poured in six points during a 10-0 Racers run that pushed the spread to 46-35 with 10 minutes to play.
Yale answered with a 10-0 burst of its own to pull back within one, but Williams threw down a dunk at the other end to spark a 9-0 surge from Murray State that made it 55-45 with 5:10 on the clock.
Duren drained a triple with 3 1/2 minutes left to slice the margin to five, but Dexter Fields countered with a trey at the other end and the Racers went 6-for-6 from the free throw line over the final 75 seconds to secure the victory.
Early on, Payne scored Murray State's first five points and helped the Racers maintain a lead throughout the first half.
The margin was eight following Williams' dunk with 7:40 left in the half before Yale closed the frame on a 12-5 swing to get within 27-26 at the break.