Ray Rice runs for a 70-yard touchdown against the Bengals. Baltimore won the AFC North and earned the No. 2 seed in the conference playoffs. (Darron Cummings/Associated Press)

The New York Giants won their way into the NFL playoffs Sunday night, beating the Dallas Cowboys to seize the NFC East crown at the end of a day in which two AFC teams lost their way into the postseason field.

The Giants got three touchdown passes from quarterback Eli Manning en route to a 31-14 triumph over the Cowboys. The Giants won the division with a record of 9-7, a game in front of the Cowboys and Philadelphia Eagles.

“NFC East champions — that’s a great thing to hear,” Giants Coach Tom Coughlin said.

Earlier Sunday, the Baltimore Ravens claimed the No. 2 seed in the AFC playoffs and the North division title with a 24-16 victory over the Cincinnati Bengals, earning a first-round bye and ensuring that a potential game against the rival Pittsburgh Steelers would be played at M&T Bank Stadium, where they were 8-0 this regular season.

In the AFC West, with another division title up for grabs, the Tim Tebow-led Denver Broncos backed into the No. 4 seed, despite losing to the Kansas City Chiefs, 7-3, when the Oakland Raiders fell to the San Diego Chargers, 38-26.

With Tebow completing 6 of 22 passes for 60 yards and a game-sealing interception, Denver (8-8) claimed a first-round home game by virtue of a tiebreaker over Oakland and San Diego and will host Pittsburgh next weekend.

The Raiders’ loss also pushed the Bengals (9-7) into the playoffs as the sixth seed even though Cincinnati’s comeback fell short against Baltimore. Cincinnati will go on the road to play Houston (10-6), the No. 3 seed, in the first round.

With the Ravens (12-4) winning, the result of Pittsburgh’s game against Cleveland was all but meaningless. The Steelers (12-4) wound up beating their AFC North rival, 13-9, and are the No. 5 seed, but lost the tiebreaker to Baltimore, which swept the season series from the Steelers.

The New England Patriots secured the No. 1 seed in the AFC, and home-field advantage throughout the playoffs, with a 49-21 victory over Buffalo. The Patriots (13-3) finished the regular season with eight wins in a row, and Tom Brady’s 5,235 yards passing were the second most in NFL history for one season.

While much of the AFC picture unfolded late in the afternoon, all but one of the NFC playoff teams were settled by the early games.

The top-seeded Green Bay Packers (15-1), who clinched the No. 1 seed and a first-round bye last week, beat the Detroit Lions, 45-41, despite five touchdowns and 520 yards passing by Lions quarterback Matthew Stafford,

The loss, coupled with Atlanta’s 45-24 win over Tampa Bay, made Detroit (10-6) the sixth seed. Detroit will play at New Orleans (13-3) in the first round. The Saints clobbered Carolina, 45-17, behind five touchdowns and 389 yards passing from quarterback Drew Brees, who finished the season with an NFL-record 5,476 yards passing. But the Saints drew the third seed when San Francisco (13-3) outlasted St. Louis, 34-27, to claim a first-round bye as the No. 2 seed and NFC West champion.

The fifth-seeded Falcons (10-6) will visit New York in the first round.

More on the NFL playoff picture:

NFL playoff schedule

Giants top Cowboys to win NFC East

Ravens clinch AFC North, first-round bye

Broncos back into AFC West title

Chargers deny Raiders a postseason berth

Patriots earn home-field advantage in AFC

49ers hold off rally, hold on to bye in NFC

Maske reported from East Rutherford, N.J.