The Titans (2-1) had grabbed the lead with 4:28 to go when Daniel Graham hauled in a four-yard pass for the go-ahead score.
But Witherspoon made sure Tennessee held on for the victory with a pick-off on a pass that was tipped by defensive tackle Jason Jones.
The Titans' Chris Johnson was stymied on the ground, with only 21 yards on 13 carries, but gained 54 yards on four receptions while Matt Hasselbeck completed 27-of-36 passes for 311 yards and two scores.
Denver (1-2) lost momentum when it failed to convert a 4th-and-goal play from the 1-yard line while holding a 14-10 advantage early in the fourth quarter.
Orton went 24-of-39 through the air for 173 yards with two touchdowns but was plagued by a pair of crucial interceptions.
Swim Week Miami Beach 2014 [PHOTOS]