The Cardinals had a chance to tie the game as time expired, but Arkansas State blocked Scott Secor's 38-yard field goal attempt.
Knighten completed 15-of-20 passes for 115 yards, one touchdown and an interception for the Red Wolves (8-5), who made their third consecutive appearance in the GoDaddy Bowl. Knighten also carried the ball 19 times for 97 yards.
Starting quarterback Adam Kennedy left in the second quarter with a knee injury.
The last three seasons have seen three different head coaches for Arkansas State. This season, Bryan Harsin left to take the head gig at Boise State in December. Former North Carolina offensive coordinator Blake Anderson is set to be the head man next season, but John Thompson served as the interim head coach in this year's edition of the GoDaddy Bowl.
Keith Wenning connected on 23-of-44 passes for 215 yards, one touchdown and an interception for the Cardinals (10-3), who fell to 0-7 in bowl games.
Jahwan Edwards carried the ball 28 times for 146 yards and a score in defeat. Willie Snead caught nine passes for 87 yards and a touchdown.
Brian Davis missed a 34-yard field goal on Arkansas State's first possession.
Ball State got on the board late in the first quarter. Snead's 9-yard TD catch with 3:07 left capped a 14-play, 89-yard drive.
Davis redeemed himself by making a 41-yard field goal on Arkansas State's first possession of the second stanza. Secor responded with a 26-yard field goal to make it 10-3.
Sirgregory Thornton's 1-yard TD run with 48 seconds left made it a 10-10 game at the half.
Davis opened the second half with an 18-yard field goal.
After the Cardinals turned the ball over on downs, Davis made a 29-yard field goal to make it 16-10.
Ball State turned the ball over on downs again, this time at the 32-yard line of Arkansas State.
Secor's 37-yard field goal early in the fourth period cut the gap to 16-13.
The Cardinals seemed poised to capture their first bowl win following a 16- play, 80-yard scoring drive. Edwards' 1-yard TD run with 1:33 to play made it 20-16 Ball State.
"The game isn't over until the time is over. So it's just hard to swallow," Edwards said. "I'm just glad we were able to score when we were at the goal line."
But the Red Wolves scored a touchdown of their own five plays later. Julian Jones and J.D. McKissic caught passes of 11 and 26 yards, respectively, before Muse's 13-yard score.
"It was awesome. I knew my teammates were behind me, and with two minutes left, they had faith in me," Knighten said. "I just wanted to do it for them, and I'm just happy that God blessed me with the ability to do it."
The Cardinals quickly moved the ball downfield -- and with the help of a 15- yard personal foul penalty on Arkansas State's Andrew Tryon -- set up for the 38-yard field goal with two seconds left.
Sunday's meeting was the first between Arkansas State and Ball State ... Kennedy completed 3-of-5 passes for 14 yards before leaving ... McKissic caught nine passes for 72 yards ... Arkansas State won a bowl game in back-to- back seasons for the first time since 1969-70.