ATLANTA — Adrian Clayborn, a former first-round pick of the Bucs, must've thought he was the one replacing Ezekiel Elliott in the backfield. The Falcons defensive end spent most of Sunday running around back there, making life miserable for former Tampa Catholic and Gator offensive lineman Chaz Green and Cowboys quarterback Dak Prescott with one of the greatest pass-rushing performances in NFL history. A solid player but hardly a star, Clayborn set an Atlanta record with six sacks and forced a pair of fumbles to lead the Falcons past the Cowboys 27-7, a game that showed just how much Dallas missed one of its key offensive players. No, not Elliott, though that was certainly a blow. After three legal reprieves, the running back finally began serving a six-game suspension for allegations of domestic abuse. The Cowboys were also without left tackle Tyron Smith, out because of groin and back injuries. Third-year player Green stepped into the spot — and had a thoroughly miserable day trying to stop Clayborn, the 20th overall pick out of Iowa in 2011. Leaving Green grasping at air, Clayborn blew by him to force two fumbles — one of which he recovered by ripping the ball away from Prescott — and surpass the team record of five sacks in a game, held by Chuck Smith and Hall of Famer Claude Humphrey. "You always envision it," Clayborn, 29, said. "I was finally in my groove." He matched the second-most sacks in NFL history; sacks became an official stat in 1982. Derrick Thomas, Osi Umenyiora and Fred Dean are the only other players credited with six in a game, while Thomas holds the league record with seven for Kansas City against the Seahawks on Nov. 11, 1990. Clayborn had more sacks in this game than any other season except for his rookie year with the Bucs in 2011, when he had 7½. He came into Sunday with two sacks on the season and 22½ over his seven-year career. "AC went crazy today," Falcons receiver Julio Jones said. Simply put, Green couldn't cope with Clayborn's speed. "It just hurts because I feel I let the team down," said Green, 25, a third-round pick in 2015. "I've just got to get better. It's on me." While Clayborn and the defense dominated the Elliott-less Cowboys, Matt Ryan threw a pair of TD passes and reached 40,000 passing yards in fewer games than any other quarterback in NFL history. Ryan has 40,073 yards in 151 games, surpassing the previous mark of 152 held by Drew Brees. Ryan hooked up with Justin Hardy on a 3-yard pass for Atlanta's first offensive touchdown in the third quarter this season. Early in the fourth, Ryan put the game away for the Falcons by tossing one to Austin Hooper for a 1-yard score.