The incident started late in the day when Patmon jarred Bryant's helmet loose during the 11-on-11 play and Bryant responded by yanking off Patmon's helmet. Patmon threw a punch and backed away, and Bryant came back with a wild left hook before teammates separated them.
The two continued fighting on the sideline before they were eventually split up by quarterback Tony Romo.
The Cowboys posted video of the exchange on their website.
Dez Bryant - Tyler Patmon Fight Full Video & Reaction MUST WATCH: http://t.co/egrkA9lI0R pic.twitter.com/oTWsb5zk1X— Dallas Cowboys (@dallascowboys) August 3, 2015
Romo was eventually able to get Bryant to move to a different part of the sideline, while Patmon stood with players and other team personnel nearby.
When practice ended a few minutes later, head coach Jason Garrett spoke briefly to Bryant, who then walked over to Patmon and hugged him while fans nearby cheered after earlier yelling at Bryant to calm down.
"I got a little bit overheated," Bryant said later. "At the end of the day, that's something that you really need for a team, on a team. I'm just trying to win ballgames."
"If you would’ve seen the play before, I was giving him a little bit of mouth, just talking a whole bunch of stuff to him,'"he said, according to the Dallas Morning News.
Cowboys owner Jerry Jones, who had already left the practice field, wasn't bothered by the skirmish.
He said he caught footage of it on television and said, "Man, you'd have thought it was CNN featuring some big event going on."
"That's training camp. That's not new," he added. "That's been happening at our training camp for years and years and years."