Keenum directed touchdown drives of 87 and 80 yards, the latter capped by a 27-yard touchdown pass to Lestar Jean. Yates, the backup to Matt Schaub the past two seasons, threw a 21-yard scoring pass to Andy Cruse and led another drive to a field goal.
Alex Tanney was under pressure and struggled in his bid get Dallas to keep a third quarterback behind Tony Romo and Kyle Orton. He was 17 of 31 for 177 yards with an interception.
Wood had 107 yards rushing, and Johnson had 79 yards and a touchdown.
Keenum mostly handed off on an 87-yard scoring drive in the first quarter - highlighted by a 29-yard run from Johnson, who went the final 5 yards for the score.
After the Cowboys slowed the run, Keenum beat them with the pass, completing 4 of 5 for 71 yards on an 80-yard drive to the second touchdown directed by the former University of Houston star. He spent last season on the practice squad after leaving UH as the NCAA's all-time leading passer.
Keenum's scoring toss to Jean came after linebacker DeVonte Holloman was called for holding on fourth-and-1 when he grabbed Johnson as he was running past him in the flat. Yates converted three third-down passes on his touchdown drive, starting with a 13-yard screen to Wood on third-and-10. The score to Cruse came on third-and-3.
Tanney was sacked seven times and sent to the ground several others, although he bounced back to get the Cowboys in position for a late touchdown before three sacks.
Tanney almost had a nifty touchdown pass to rookie tight end Gavin Escobar, who couldn't get a second foot down in the corner of the end zone.
The second-team defense for Dallas has been pushed around all preseason. Wood had 78 of Houston's 120 first-quarter yards rushing, and he would have had more than 100 without a holding penalty that nullified a 49-yard scoring run.
Much like Keenum and Yates behind Schaub, Johnson and Wood are working to be a backup to Arian Foster, with Ben Tate also in the mix. And both looked solid.
Wood had a 5.6-yard average that would have been substantially higher without penalties. Johnson averaged 4.6 per carry.
The Cowboys didn't really get a chance to settle the battle for their backup running back because Lance Dunbar missed his second straight game with a sprained foot.
Phillip Tanner had 35 yards on six straight carries to start the game, but didn't return after the first series. Joseph Randle finished 47 yards on 10 carries, including an 18-yard run on a drive that ended with a 38-yard field goal by Dan Bailey.
The regular season begins Monday, September 9, against San Diego. You can catch the game on ABC13.