Dallas (1-1) had three holding penalties in the first five plays of an opening drive that stalled. Then Romo completed all three passes, including a pair to trusty tight end Jason Witten, before the scoring run from Morris, who had 13 carries for 85 yards.
Romo was 4 of 5 for 49 yards, and the Dallas offense had 300 yards at halftime.
"It was a good start. We needed that," Witten said. "It's been a long offseason. We have Tony leading the way. We had a lot of energy."
Tannehill, who played late into the first half with the Dolphins (1-1) trying to move past a rough opener for the first-team offense last week, had scoring passes of 13 and 3 yards to Stills. Tannehill led another drive inside the 5 that ended on downs and finished 12 of 20 for 162 yards.
"I liked the mentality that he had going into that first half," first-year coach Adam Gase said. "I liked the fact that the ones wanted to stay in and do another series. That's what I wanted to see."
Prescott has two touchdowns passes in each of the two preseason games and is 22 of 27 for 338 yards without an interception after completing his first eight passes following a 10-of-12 showing in his NFL debut against the Los Angeles Rams last week.
The fourth-round pick out of Mississippi State had a 20-yard scoring run and a 1-yard sneak that was held up on review. Prescott tossed a short touchdown pass to Brice Butler the play after a 58-yarder to the speedy wideout.
Prescott had an overthrow for what would have been his first interception in the second quarter, but it was wiped out by a roughing-the-passer penalty against Andre Branch.
"It's been a great start for him, and he's excited about it," Romo said. "You just keep building on it every day, but you can't ask for a better start."
Copyright 2016 by The Associated Press