The victory was the fourth straight at home for the Giants (5-1) - one more than they had last season - and it sent the 49ers (2-5) to their fourth straight loss.
This one wasn't pretty for either team, especially San Francisco, which turned over the ball three times, allowed six sacks, a safety and had 13 penalties for 134 yards. Combined it handed New York 19 points.
The Giants had their moments, too. On the verge of building a 17-point lead late in the third quarter, Manny Lawson blocked John Carney's field goal attempt and Nate Clements returned it 74 yards for a touchdown, cutting the lead to 24-17.
Carney atoned moments later with a 48-yard field goal, and the defense iced the game with a sack that led to a safety when receiver Josh Morgan kicked the ball out of his end zone.
New York never trailed in rebounding from a loss in Cleveland on Monday night that ended its 11-game road winning streak, 12 including the Super Bowl win over New England.
Jacobs gave New York the lead with a 26-yard first-quarter run.
He stretched it to 14-3 with a 2-yard run early in the second quarter on a drive in which Clements was flagged for 46 yards in penalties with a pass interference and an unsportsmanlike conduct penalty.
A 30-yard touchdown pass from J.T. O'Sullivan to Morgan closed the gap to 14-10, but Johnson's first interception and return to the 9-yard line led to a chip-shot field goal by Carney, who got the starting nod ahead of Lawrence Tynes.
Johnson's second interception in the end zone late in the half prevented the 49ers from tying the game.
Manning, who was 16-of-31 for 161 yards, stretched the lead to 24-10 early in the third quarter after the 49ers botched a handoff deep in their territory and Mathias Kiwanuka recovered at the San Francisco 18.
Manning hit Plaxico Burress on a 6-yard scoring pass.
New York seemed on the verge of blowing the game open late in the third quarter when a 35-yard screen pass to Derek Ward and a pass interference penalty put the ball deep in San Francisco territory. However, Jay Alford bounced his snap to Jeff Feagles and that led to the block that made the game interesting.
The Giants, who played without middle linebacker Antonio Pierce (quad), were almost as bad as San Francisco, collecting 11 penalties for 80 yards.
