It was the fourth Super Bowl triumph for the Giants, who also defeated the Patriots in the 2008 NFL championship match and captured the crown in 1987 and 1991.
Before a crowd of 68,658 at the dome-enclosed stadium where his older brother Peyton stars for the Indianapolis Colts, New York's Eli Manning guided the Giants on an 88-yard touchdown drive in the closing minutes capped by Bradshaw's scoring run.
"It just feels good to win a Super Bowl no matter where you are or what stadium it is," Manning said.
Manning was named the game's Most Valuable Player after completing 30-of-40 passes for 296 yards and a touchdown.
New England took over needing a touchdown in the dying seconds but Tom Brady, who had already set records in the game for consecutive completions and completions in a row at the start of a Super Bowl, could not pull off a miracle.
Brady made two late throws to the end zone from midfield, the last on the game's final play, but New York defenders made certain they would not be denied a fairytale finish after starting the season 7-7 and winning six games in a row for the title when one defeat would have doomed their unlikely title dream.
Clinging to a 17-15 lead, the Patriots were shut down near midfield and forced to punt, the Giants taking the ball at their own 12-yard line with 3:46 to play.
Manning completed a 38-yard pass to Mario Manningham that was confirmed on a video replay challenge to put New York at midfield, hit Manningham again for another 16 yards and Hakeem Nicks for 14 more to reach New England's 18-yard line with 2:00 remaining.
Three plays later, Bradshaw ran untouched into the end zone for a touchdown that gave the Giants a 21-17 lead.
A two-point conversion run failed, leaving 57 seconds for the Patriots to try and score a touchdown to win the game.
The Patriots got their opportunity, but the Giants were not to be denied.
"At half-time I said we can play better than this. They agreed," Giants coach Tom Coughlin said. "We came out energised in the second half and the rest is history."
Brady threw a four-yard touchdown pass to Danny Woodhead with eight seconds to play in the second quarter to give the Patriots a 10-9 half-time lead, the score capping a 96-yard drive.
The Patriots began the second half with another touchdown march, this one of 79 yards and finished off by Brady's 12-yard touchdown pass over the middle to Aaron Hernandez to put New England ahead 17-9 only 3:40 into the third quarter.
New York answered on field goals of 38 and 33 yards by Lawrence Tynes to pull within 17-15 entering the fourth quarter.
Earlier, two Patriots penalties in the shadow of their own end zone helped the Giants seize a nine-point lead after only 11:36 had elapsed.
New England had to settle for a 29-yard Stephen Gostkowski field goal to pull within 9-3 just 72 seconds into the second quarter after Jason Pierre-Paul batted down a Brady pass to shut down a 60-yard drive.