New York produced 405 yards of offense and built a 20-0 lead at halftime. The Giants improved to 2-1 with their second straight win following a season-opening setback to the Dallas Cowboys. Carolina fell to 1-2.
Manning completed 27-of-35 passes and opened the scoring by hitting Martellus Bennett with a 14-yard throw on New York's opening possession. The Giants set the tone for the game by driving 80 yards in eight plays the first time they had the ball.
The other two New York touchdowns came from Brown on a pair of 1-yard runs.
It was a breakout game for Brown, who has bounced around with five teams since being drafted by the Giants in 2009 and who until Thursday had carried the ball only 15 times in his career.
Brown's 113 yards against the Panthers came on 20 carries.
Tynes kicked field goals of 47, 49, 30, 36 and 27 yards, the last of them coming with 69 seconds left in the game. Nine of Manning's completions went to Ramses Barden for 138 yards.
Newton was 16-of-30 for 242 yards. He scored Carolina's only touchdown on a 1-yard run in the third quarter that cut the Panthers' deficit to 23-7.