LOS ANGELES — C. J. Anderson rushed for 123 yards and two touchdowns while his teammate Todd Gurley rushed for 115 yards and another touchdown in the first playoff victory for the Los Angeles Rams in 14 years — a 30-22 win over the Dallas Cowboys in the N.F.C. divisional round on Saturday night.

Gurley and Anderson punished the Cowboys’ normally sturdy run defense and sent the second-seeded Rams to the conference championship game for the first time in 17 years. Los Angeles gained a franchise playoff-record 273 yards on the ground — also the most ever allowed in the postseason by the Cowboys, who were playing in their N.F.L.-record 63rd postseason game.

The long-struggling franchise had won only one postseason game since its last trip to the Super Bowl, as the St. Louis Rams in February 2002, but it has had a spectacular turnaround under Sean McVay, its 32-year-old coach.

Ezekiel Elliott rushed for a touchdown and Amari Cooper caught an early scoring pass for the Cowboys (11-7), who have not won a playoff game on the road in 26 years. After winning the N.F.C. East and beating Seattle last week, Dallas lost in the divisional playoff round for the sixth consecutive time and fell short of its first trip to the N.F.C. Championship game since January 1993.