Placeholder Steve Weatherford corralled a low snap and set it up for Tynes, whose boot 7:06 into the extra frame sent the Giants into the Super Bowl against New England in a rematch of the 2007 championship game.
The Patriots, who lost to New York 17-14 in that game, reached the Super Bowl with a victory over Baltimore earlier Sunday.
Eli Manning went 32-of-58 through the air for 316 yards, two touchdowns and no interceptions while surviving six sacks for New York, which improved to 5-0 in NFC championships.
Victor Cruz made 10 grabs for 142 yards in the victory.
Alex Smith completed 12-of-26 passes for 196 yards and a pair of TD tosses for the 49ers.