The Cowboys' third straight win - a comfortable 42-7 result over the Indianapolis Colts - saw them to the title after the Philadelphia Eagles' 27-24 loss to the Washington Redskins on Saturday.
Jason Garrett's men won the division for the first time since 2009.
Tony Romo threw four touchdown passes for Dallas, as he completed 18 of 20 pass attempts to drive his side 218 yards.
Cowboys tight end Jason Witten had 90 yards to his name off seven receptions, including one touchdown, while wide receiver Terrance Williams' two catches were both six-pointers.
The New England Patriots secured a bye past the first round of the post-season, after edging the New York Jets 17-16.
Jonas Gray's one-yard TD rush put the Patriots ahead early in the final quarter, and New England will be at home for their first play-off game should the Denver Broncos lose to the Cincinnati Bengals on Monday night.
The Green Bay Packers are post-season bound after they bounced back to winning ways with a 20-3 result over the Tampa Bay Buccaneers.
The Packers are level with the Detroit Lions in the NFC North with 11-4 records heading into their regular season clash on Sunday - in what has become a division play-off.
Detroit go into the clash off four straight wins, after handling the Chicago Bears 20-14.
The NFC South crown will also come down to one game - between the Carolina Panthers and Atlanta Falcons, after the latter eliminated the New Orleans Saints.
The Falcons were 30-14 winners over the Saints, while Carolina go into their post-season decider in winning form too - after edging the Cleveland Browns 17-13.
Super Bowl champions the Seattle Seahawks climbed top of the NFC West - level on an 11-4 record with the Arizona Cardinals - after beating their title rivals 35-6.
The Pittsburgh Steelers also booked their post-season ticket, with a 20-12 victory over the Kansas City Chiefs.
There was plenty of tension in the New York Giants' 37-27 victory over the St Louis Rams, with three players ejected during the second quarter after a brawl.
The Houston Texans beat the Baltimore Ravens 25-13, the Miami Dolphins edged the Minnesota Vikings 37-35 and the Oakland Raiders were 26-24 winners over the Buffalo Bills.