Matthew Stafford revelled in "stealing somebody's soul" after he helped the Los Angeles Rams end the Tamp Bay Buccaneers' playoff hopes.

The Rams prevailed 30-27 over last season's Super Bowl champions on Sunday to reach the NFC Championship game, which will be a matchup between two underdogs after the San Francisco 49ers' win over the Green Bay Packers.

Yet it could very well have gone badly wrong for Los Angeles, who had led 27-3 until a Tom Brady-inspired comeback from the Bucs in the final quarter.

Brady connected with Mike Evans for a 55-yard touchdown pass, with the possibility of a turnaround that would rank as the joint-fourth largest in postseason history coming into view.

Evans' score made the game 27-20 and another Rams mistake allowed the Bucs to level the scores through Leonard Fournette.

Yet Stafford had other ideas, with the 33-year-old – who joined from the Detroit Lions ahead of this season – combining with wide receiver Cooper Kupp to set up a Matt Gray field goal.

"In my mind, I live for those kinds of moments," said Stafford, who has now made 43 game-winning drives in the fourth quarter or overtime. That is the most of any player since the QB first featured in the NFL in 2009.

"I would have loved to have been taking a knee up three scores, but it's a whole lot more fun when you've got to make a play like that to win the game and just steal somebody's soul.

"That's what it feels like sometimes where they're sitting there going, 'Man, we just had this great comeback.' And you get to reach in there and take it from them. That's a whole lot of fun."

Stafford threw for 366 yards against Tampa Bay, a high mark for the season, besting his previous high of 365 set against the Seattle Seahawks in Week 5 and bringing up the third-highest yardage in a single postseason game in Rams history.

He also threw for two touchdowns, rushed another and registered a pass completion rate of 73.7 per cent, finding his target with 28 of 38 attempts.

One of those touchdown passes was a 70-yard combination with Kupp, who led the way in the regular season for receiving yards (1,947), receiving touchdowns (16) and receptions (145).

However, Kupp was not happy with how the Rams' offense performed in the midst of Tampa Bay’s fightback.

"As an offense, we first and foremost did a terrible job of executing for this team in the second half," Kupp said.

"We can't do the things that we did. Put our defense, our team in a really bad spot."

Yet head coach Sean McVay was happy to reflect on a thrilling win, saying: "That's why you play four quarters and try to finish that game out.

"That was something else. That was something else.

"Those guys did a great job. I thought Matthew Stafford was unbelievable throughout the whole day. Just his poise, his command, his decision-making."