New Tennessee starting quarterback Jake Locker threw two first-half touchdown passes to give the Titans the lead, but the Cardinals rallied to go in front in the fourth quarter on scoring runs by William Powell and Javarris James.
Arizona had the ball and the lead inside the 6-minute mark, but quarterback Ryan Lindley fumbled the ball away on a sack and Harper scored one play later.
Locker, the eighth player chosen in the draft last year, was named the Tennessee starter this week. He completed 11-of-20 passes for 134 yards and threw touchdowns of 10 yards to Kendall Wright and 28 yards to Nate Washington.
Arizona is 2-1 in exhibition play and Arizona is 1-3.