The Giants' first shutout since 1996 opens up the race for top spot in the intriguing NFC East with the Washington Redskins joining the Giants at 8-6 after a 38-21 win at the Cleveland Browns.
The Houston Texans secured the AFC South title with a 29-17 win over divisional rivals Indianapolis while the Baltimore Ravens suffered their third consecutive loss of the season with a 34-17 defeat at home to the Denver Broncos.
Packers quarterback Aaron Rodgers threw three touchdown passes to James Jones as Green Bay moved to 10-4 putting them out of reach of the Bears, who slip to 8-6.
After their fifth loss in six games, Chicago's only hope of the play-offs is with a wild-card - a sorry state of affairs after they began the season 7-1.
Jones scored on 29 and eight yard pass plays in the second quarter as the Packers took the lead after a 15-yard Jay Cutler pass to Bears receiver Brandon Marshall had opened the scoring.
After the third Rodgers-Jones combination in the third quarter, the Bears could manage only two field goals as their old rivals sealed their second successive divisional title.
With two games left to play, the NFC East is suddenly the most fascinating division in the league with the Giants now overtaken by the Redskins who have the tie-break advantage in divisional games.
New York have won just two of their last six games and along with the Redskins.
Atlanta's victory was a statement of their intent in the post-season as Mike Smith's team confirmed their status as the top team in the NFC.
Matt Ryan threw three touchdowns and 270 yards as the Falcons dominated from the outset, going 14-0 up in the first quarter thanks to a one-yard Michael Turner run and a 12-yard Ryan pass to tight end Tony Gonzalez.
Receiver Julio Jones caught a 40-yard touchdown pass from Ryan in the third and then finished off with a three-yard collection in the final quarter.
The question hanging over the Redskins as they travelled to Cleveland was whether they would be able to cope with the absence of injured quarterback Robert Griffin III.
With another rookie, Kirk Cousins, given the stand-in role, fears were legitimate but 329 passing yards and two touchdowns from the man picked 102nd overall in this year's draft earned a vital win.
Making his first career start after Griffin's knee sprain, Cousins used a 54-yard scoring pass to Leonard Hankerson to cancel out a six-yard Trent Richardson rushing touchdown in the first.
Cousins found Hankerson again with a two-yard pass in the third as the Redskins secured their fifth consecutive win with touchdown runs from Evan Royster and Alfred Morris.
The Texans (12-2) had already assured themselves of a place in the post-season but their win secured them the AFC South title. The loss means quarterback Andrew Luck and Colts are not yet sure of a wild-card place although at 9-5 they remain in a strong position.
Running back Arian Foster rushed for 165 yards for Houston while Andre Johnson had 151 yards receiving and scored on a three-yard Matt Schaub pass in the first quarter to put the Texans 10-0 up.
The game turned decisively in Houston's direction in the second quarter when Bryan Braman returned a blocked punt eight yards for a touchdown.
The contrasting form of Denver and Baltimore continued with Peyton Manning and the Broncos enjoying a ninth straight win in a 34-17 victory that dropped the Ravens to 9-5.
The Ravens made it to the play-offs for the fifth straight season thanks to Dallas' overtime victory over the Pittsburgh Steelers. They progress with two games remaining in the regular season even though they suffered their third consecutive loss.
Drew Brees threw for four touchdowns as the New Orleans Saints (6-8) crushed the Tampa Bay Buccaneers 41-0.