The pass came on the first play of the second overtime
In a contest that featured a handful of momentum-changing plays, Delhomme,on 3rd-and-14, found Smith in stride on a slant. Free safety Jason Sehorn slipped, and Smith raced untouched to the end zone.
Before becoming th first postseason game to reach double overtime since 1987, each team squandered a chance to win in the first OT.
John Kasay appeared to give the Panthrs the win with a 40-yard field goal with under 10 minutes left. But the Panthers were charged with a delay of game and Kasay hooked a 45-yarder.
The Rams drove into Panthers territory but Jeff Wilkins' 53-yard field goal fell short.
Trailing 23-20, the Rams, trailing 23-20, moved inside the Panthres 20. But with 30 seconds to go and a timeout in hand, Coach Mike Martz opted for a field goal to send thgame into overtime.
Carolina (12-5) will meet Philadelphia or Green Bay in the NFC championship game next Sunday.
The Rams (12-5) had their 14-game home winning streak stopped.