Austin also caught a 59-yard scoring pass from Romo and finished with 10 receptions for 250 yards.
Romo was 20-of-34 for 351 yards.
Tashard Choice ran for 92 yards and a touchdown for the Cowboys (3-2).
Matt Cassel completed 23-of-41 passes for 253 yards and two touchdowns for Kansas City (0-5).
Cassel connected with Mike Vrabel on a 1-yard scoring play and with Dwayne Bowe on a 16-yarder.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut