Faulk scored on a 1-yard dive with 3:27 left to put the Rams ahead of the New Orleans Saints 26-14 for the record. He then ran over to the stands and presented the ball to a female family member.
The touchdown was set up by a 42-pass to Torry Holt to the Saints 1.
The star running back, who missed two games during the season with minor knee surgery, ran untouched for a 9-yard score with 2:45 left in the third quarter, his second touchdown of the game. Faulk also scored on a 13-yard pass from Kurt Warner in the first period.
Smith scored 25 times for Dallas in 1995.
This year, Faulk became the first player in NFL history to score four touchdowns in a game three times in a season. He's also the first player in league history to score four touchdowns in back-to-back games.
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