Romo amassed 198 yards on 9-of-13 passing. Harris finished with three receptions for 118 yards.
Harris hauled down scoring passes of 61 and 38 yards from Romo in the first quarter.
Sam Bradford started for the Rams and gained 64 passing yards on 6-of-17 attempts.
Kellen Clemens, meanwhile, passed for 69 yards on 6-of-9 attempts with a touchdown.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes