Shorts got past defender Joe Haden on the play and was all alone for the 20-yard scoring strike.
Henne made good on 22-of-40 passes for 195 yards with two touchdowns as the Jaguars (3-9) won a third straight road game.
Shorts finished with six grabs for 64 yards while Clay Harbor and Marcedes Lewis each corralled a TD pass.
The Browns (4-8) were led by Josh Gordon with 261 receiving yards and a pair of touchdowns on 10 catches.
He was coming off a 237-yard performance against Pittsburgh, making him the first player in NFL history to have back-to-back games with 200 or more receiving yards.
Brandon Weeden compiled 370 aerial yards with three touchdowns and two interceptions on 24-of-40 efficiency as Cleveland lost a third straight.