Trailing 20-17 with 3:15 remaining, Manning hit Boss with a short pass and the tight end broke a tackle, found open space and sped into the end zone with the decisive score.
The Giants (7-4) followed that up by stopping Jacksonville's attempt to answer the score. Jaguars quarterback David Garrard was sacked on three consecutive plays. He fumbled the ball on the final sack with just under 90 seconds left to seal New York's win.
Manning went 14-of-24 through the air for 226 yards and a pair of TDs.
Boss finished with three catches for 74 yards and Mario Manningham made three grabs for 561 yards and a score for the victors.
Jacksonville (6-5) was led by Garrard, who went 20-of-35 passing for 162 yards, one TD and one interception.