Downs was signed as an undrafted free agent by the Dallas Cowboys after the 1981 NFL Draft. He wasn't selected because he suffered a pinched nerve in his shoulder as a senior, which affected his play and earned him a reputation for not being aggressive. He was so impressive in training camp, that he became the third rookie in Cowboys history to begin the season as a starter, after free safetyRandy Hughes suffered a dislocated right shoulder and Dextor Clinkscale an Achilles injury in pre-season. His performance also allowed the team to move Dennis Thurman from free safety to cornerback. He was a playmaker from the start, intercepting a Joe Theismann pass in the first quarter of a 26–10 win against the Washington Redskins in the season opener. He missed the second game with a hamstring injury. He had a stretch of three straight games with an interception and would go on to intercept a total of 7 passes, while contributing to the Cowboys leading the NFL in interceptions and setting a franchise record. Against the Chicago Bears, his 15 total tackles and 13 solo tackles were club season highs. He tallied 110 tackles, 72 solo tackles, 11 passes defensed and one fumble recovery. He also intercepted a pass against the Tampa Bay Buccaneers in the playoffs. He was named to the All-Rookie team. In 1982, he posted 70 tackles, 3 fumble recoveries and one interception. Against the Tampa Bay Buccaneers, he had 15 tackles, he forced a fumble and recovered another one at the two-yard line with five seconds left to preserve a 14-9 win. Against the Houston Oilers, he recovered a fumble and returned it 86 yards for a touchdown. In 1983, he registered 111 tackles, 4 interceptions, 1.5 sacks and 3 forced fumbles. He returned a fumbled kickoff 10 yards for a touchdown in the third game against the New York Giants. In 1984, he had his best season, collecting 136 tackles, 96 solo tackles, 7 interceptions, 3.5 sacks, 13 passes defensed, 3 forced fumbles and 2 fumble recoveries. Against the New Orleans Saints, Downs helped the team rallied back from a 27-6 fourth-quarter deficit to win 30–27 in overtime, by making 9 tackles, 2 interceptions, one pass defensed, one fumble recovery and also recovered a blocked punt. Even though he wasn't voted to the Pro Bowl, he received second-team All-Pro and All-NFC honors. During the 1985 season, quarterbackDanny White nicknamed Thurman along with Downs and cornerbacks Everson Walls, Ron Fellows, "Thurman's Thieves", for their opportunistic play in the secondary. Downs was named a defensive co-captain, posting 116 tackles, 69 solo tackles, 3 interceptions, 3 fumble recoveries and 2 forced fumbles. In 1986, he recorded 101 tackles, 6 interceptions, one fumble recovery and one blocked punt. The next year, he had 86 tackles, 4 interceptions and one fumble recovery. In 1989, with the arrival of Jimmy Johnson, he was released as part of a youth movement on May 5. During his time with the Cowboys, Downs helped anchor the secondary for most of the eighties decade. He was considered one of the best tacklers in the NFL, leading the team secondary for seven consecutive seasons, making over 100 tackles in 5 seasons and leading the team in tackles in 3 seasons. He finished with 34 interceptions and 3 touchdowns.
Phoenix Cardinals
On September 26, 1989, he was signed as a free agent by the Phoenix Cardinals, after Lonnie Young broke his left shoulder in the season-opener. He reunited with Gene Stallings and Dennis Thurman. In the eight game of the season, the Cardinals came into Texas Stadium and defeated the Cowboys 19-10. He was waived on October 31, after appearing in 5 games with one interception.