[caption id="attachment_112849" align="alignleft" width="233"] Green Bay Packers' defensive back Kentrell Brice (No. 29) breaks up a pass intended for Dallas Cowboys' wide receiver Terrance Williams (No. 83) during the second half of their NFL divisional playoff game in Arlington, Texas, Sunday. — AP[/caption]LOS ANGELES - Mason Crosby kicked a last-gasp field goal as the Green Bay Packers downed the Dallas Cowboys 34-31 in a thrilling NFL playoff battle Sunday. Crosby held his nerve superbly to kick the winning three-pointer from 51 yards with just three seconds left on the clock in the final twist of an epic duel at the AT&T Stadium. Green Bay will now play the Atlanta Falcons next Sunday in the National Football Conference Championship game for a place in the Feb. 5 Super Bowl in Houston. Elsewhere Sunday, the Pittsburgh Steelers won their ninth straight with an 18-16 win over the Kansas City Chiefs to book a spot in the AFC Conference game against the New England Patriots. Crosby's winning field goal came after quarterback Aaron Rodgers connected with Jarad Cook with a 36-yard pass at the Dallas 32. Cook was initially adjudged to have gone out of bounds but the call was over-ruled, handing the Packers field position and Crosby his shot at immortality. Packers coach Mike McCarthy paid tribute to Rodgers' ability to lead the game-winning drive with just seconds left. The finale capped a pulsating closing two minutes. Crosby had kicked a 56-yard field goal to put Green Bay 31-28 ahead only for the Cowboys - who had rallied back from a 21-3 first-half deficit - to tie it at 31-31 with a 52-yard Dan Bailey effort. The Cowboys - the top seeded team in the NFC after a 13-3 regular season - were left ruing a shaky first half display which saw Green Bay power ahead. Cowboys rookie quarterback Dak Prescott and running back Ezekiel Elliott both failed to exert control in the early stages but it was the Dallas defense's inability to stymie Rodgers that proved fatal. After Bailey had kicked a field goal to put Dallas 3-0 ahead, Rodgers took over. The Packers quarterback connected with namesake Richard Rodgers on a 34-yard pass for Green Bay's opening touchdown. Dallas was then forced to punt its next possession, and Rodgers duly marched his team 90 yards upfield to allow Ty Montgomery to rush over from three yards. Another Dallas punt was followed by another relentless Green Bay drive which went 80 yards before Montgomery barrelled over from one yard to make it 21-3. Dallas responded with a quickfire touchdown over their own, Prescott finding receiver Dez Bryant with a 40-yard touchdown pass that cut the score to 21-10. A further Bailey field goal gave Dallas hope at 21-13 but Green Bay were quickly back into their rhythm early in the third quarter when Rodgers found tight end Cook for the simplest of three-yard touchdown passes to restore the Packers' 15-point cushion. Dallas then got on top with Jason Witten and Bryant scoring touchdowns before Prescott rushed for a two-point conversion to tie it 28-28. But with just minutes remaining, Crosby was to prove the hero for Green Bay in his duel with Bailey. The Steelers rode the strong right leg of kicker Chris Boswell to beat the Chiefs. Boswell made all six of his field goal attempts, while the Steelers' offense produced plenty of yards, but no touchdowns. The Steelers finished with 389 total yards on offense, with Le'Veon Bell running for 170 yards and Antonio Brown registering 108 receiving yards. The victory sends the Steelers to the AFC Championship Game next Sunday against the Patriots at Gillette Stadium in Foxborough, Massachusetts. It will be the 16th time the Steelers have advanced to the AFC Championship Game. They won eight of the previous 15 games, including their most recent appearance in the 2010 season when they beat the New York Jets 24-19. Pittsburgh faced Tom Brady's Patriots twice before in the title game (2001, 2004), losing both times. This season, the teams met on Oct. 23 in Pittsburgh, with the Patriots winning 27