The Dolphins (4-6) are likely to miss the playoffs for the seventh year in a row. They're 3-3 since coach Joe Philbin was fired and replaced by Campbell.
"I want to keep Dan around," Tannehill said. "He does a great job. He's exciting. Everyone in our locker room believes in him. But as players we've got to go out and do a better job."
The Dolphins might need to sweep their final six games to make the playoffs.
"We need a win badly. Badly," Campbell said. "As far as I'm concerned we still hold the cards. It's all about winning. Let's just go win. Let's get back on track."
To do so will require more offense. Tannehill's unit had the ball for only 21 minutes, went 1 for 10 on third-down conversions and gave up a score for the fourth game in a row. Dallas linebacker Rolando McClain scored the game's first points and his first career touchdown on a 12-yard interception return.
Meanwhile Miami's run defense, ranked next to last in the NFL, allowed 166 yards. Darren McFadden ran for 129, and Robert Turbin, who joined the Cowboys on Wednesday, added 35 yards on seven carries.
"We've got to stop the run," Miami defensive tackle Ndamukong Suh said. "We didn't do a good enough job in that area. That's pretty much as simple as it gets. It came down to missing tackles, missed assignments."
Campbell took responsibility for a flurry of flags against the Dolphins. They were penalized nine times for 74 yards.
"I've got to do a better job of holding these guys accountable in practice," he said.
Romo returning from a collarbone injury to throw for two scores, and the Cowboys (3-7) won for the first time since he was hurt in Week 2. They snapped a seven-game losing streak.
"Winning," Romo said, "is going to put a little more pep in everyone's step."
The Cowboys' first scoring threat ended with an interception by Brent Grimes, but Romo soon settled down and showed his characteristic creativity. A left-handed desperation completion allowed him to avoid a safety on the Cowboys' opening possession.
The game matched a pair of last-place teams and looked it at times. Dallas committed 10 penalties and Miami nine.
A dance celebration by Bryant and Williams following a score prompted an unsportsmanlike conduct penalty that helped Miami score a touchdown in the final seconds of the first half.
But Bryant beat a linebacker and a safety for the touchdown that put the Cowboys ahead to stay, 21-14, on the first play of the fourth quarter.
The Cowboys mounted an 8 1/2-minute drive for their first offensive score. A third-down holding penalty on cornerback Jamar Taylor allowed the Cowboys to keep the ball, and he was beaten deep by Williams on another third down for the TD.
"I put this loss on me," Taylor said.
Tannehill went 13 for 24 for 188 yards, and Miami was again unable to generate a consistent running attack. Lamar Miller averaged 6.3 yards per attempt but carried only seven times.
Notes: Neither team reported any injuries. ... Christopher Ruiz, a civilian contractor who died in Afghanistan in October, was honored during a timeout in the Dolphins-Cowboys game. Ruiz was the stepbrother of Dolphins receiver Rishard Matthews. ... Former Dolphins coach Don Shula received his new Pro Football Hall of Fame ring in a halftime ceremony.