Givens caught nine passes and one touchdown his rookie year for the New England Patriots in 2002, and improved in each of the next two seasons. He posted 34 catches and lead his team with six touchdowns in 2003 and 56 catches in 2004 despite scoring just three times. His best performances in his career came in the postseason. Beginning with the 2003 AFC Championship Game against the Indianapolis Colts, Givens scored at least one touchdown the Patriots' next seven playoff games, including both Super Bowl XXXVIII and Super Bowl XXXIX. In 2005, Givens caught a career-high 59 passes and was the Patriots' number two receiver for the second year in a row.
Givens was the Patriots' record holder in postseason touchdown receptions til New England's 2015 season, before being surpassed by Rob Gronkowski who scored his eighth playoff touchdown against Kansas City Chiefs in the Divisional Round of the NFL playoffs on January 20th, 2016, and is tied for the NFL record in most consecutive post-season games with a touchdown reception.