Brady's 16th straight completion going back to the first half found Hernandez across the middle and the second-year tight end broke a tackle by safety Deon Grant to get into the end zone.
After completing his final 11 passes in the first half -- including 10 on a 96-yard touchdown drive that tied a Super Bowl record -- Brady was 5-for-5 on the 79-yard drive that opened the third quarter.
Brady's 16 straight completions tied his own postseason record and broke the Super Bowl record of his idol, Joe Montana, during Super Bowl XXIV in 1990. Brady's 16 postseason wins are tied with Montana for most playoffs victories by a quarterback in NFL history.
Brady also passed Kurt Warner (1,156) to take the all-time lead in Super Bowl passing yards.
The Giants responded to Hernandez's touchdown with a 45-yard drive that ended in a 38-yard field goal by Lawrence Tynes to get them within 17-12. The drive was set up by Jerrel Jernigan's 34-yard kickoff return.
New England went 3-and-out after that, with Giants defensive end Justin Tuck sacking Brady on third down and driving the quarterback's left shoulder into the turf.
New York, with good field position at the Patriots 48, turned around and kicked another field goal to get within 17-15. Tynes was good on the 33- yarder.
Earlier, Brady threw a four-yard touchdown pass to Danny Woodhead to end the 96-yard drive near the end of the first half and give the Patriots a 10-9 lead going into the break.
Brady was 10-for-10 on the drive and completed his last 11 passes in the half. The 96-yard drive, coming after the Patriots were pinned in deep by a punt, tied a record for the longest in Super Bowl history.
Giants quarterback Eli Manning was also completing most of his passes.
In fact, Manning started the game 9-for-9 and threw a two-yard touchdown pass to Victor Cruz to give New York a 9-0 lead after the first quarter.
New York also got two points on a safety when Brady was called for intentional grounding on New England's first play from scrimmage.
Brady's pass, under pressure, was thrown 45 yards downfield from the front of the end zone with no receiver in the vicinity and was the sixth safety in Super Bowl history.
Manning led the Giants on a 78-yard drive after that, which included a penalty on New England for too many men on the field that reversed a fumble by Cruz. The drive was capped by Manning's short pass to Cruz behind two defenders with 3:24 left in the quarter, making it 9-0.
The Giants ran 19 of the game's first 20 plays from scrimmage as New England had trouble getting out of its own way early.
But the Patriots started a 60-yard drive that spanned the first and second quarters and ended in Stephen Gostkowski's 29-yard field goal, pulling them within 9-3.
The game is a rematch of the 2008 Super Bowl, which the Giants won, 17-14, on Plaxico Burress' 13-yard touchdown catch with 35 seconds remaining. The game- winning drive, led by MVP Manning, included David Tyree's famous helmet catch.
The game is also a rematch from Week 9 this past season. Manning threw a TD pass in the final minute of that one to give the Giants a 24-20 win over the Patriots.