Vinatieri's heroics came after Jaguars kicker Jason Myers missed a 53-yard field goal that could have won it at the end of regulation for the Jaguars and then another 48-yard attempt in the overtime period. Vinatieri hit his game-winning 27-yard kick on the ensuing drive.
Vinatieri recognized the continuity that has enabled him to surpass 1,000 points with the Colts, for whom he has kicked since 2006 after 10 seasons with the New England Patriots.
"That means I have been on this team for a long time, a part of a great organization, a part of a lot of great teams in this locker room and a lot of opportunities to get on the field," Vinatieri said.
Vinatieri hit three field goals from 54, 32 and 27 yards, as well as one extra point against the Jacksonville Jaguars, giving him 1,004 points as a member of the Colts. Heading into the game Sunday, Vinatieri had 994 points.
The Colts played without Andrew Luck, who missed the first game of his NFL career. Luck was ruled out with a shoulder injury and replaced by Matt Hasselbeck, who finished 30-of-47 for 282 yards and a touchdown in the victory.
Vinatieri was already one of two players in the NFL to score 800 or more points with two teams. Vinatieri also moved past John Carney to be fourth all-time for field goals made.
Vinatieri is now the Colts' all-time leading scorer after passing Mike Vanderjagt, who had 995 points.
ESPN Colts reporter Mike Wells and The Associated Press contributed to this report.