The victory put the Cowboys at 4-0 for the first time since their Super Bowl season of 1995.
Crayton had seven catches for 184 yards while Romo completed 21-of-33 passes for 339 yards.
Romo hit Crayton twice in the third quarter for scores of 59 and 37 yards. Romo also threw a scoring pass to Jason Witten in the third, while Julius Jones ran one in from 2 yards out in the second quarter to open the scoring.
The visiting Rams (0-4) managed 125 yards of total offense to 331 for Dallas, and converted just three of a dozen third-down opportunities.
Marc Bulger completed 11-of-24 passes for 114 yards and was intercepted once.
The Rams only touchdown came in the second quarter on an 85-yard punt return by Dante Hall that tied the score, 7-7.
Hall leads the NFL with six career TDs on punt returns.
Swim Week Miami Beach 2014 [PHOTOS]