"Just fun to watch him do his thing, whether it's offensively, the big throw he made defensively," Cardinals manager Mike Matheny said.
It was the longest postseason game for the Dodgers since the 1916 World Series, when Babe Ruth pitched all 14 innings to lead the Boston Red Sox past Brooklyn.
This one also tied for the longest series opener in postseason history, according to STATS. Boston and Cleveland played 13 innings in their 1995 AL division series, with the Indians winning 5-4.
"That's a preview. Today was a good game and that's what it's all about. They didn't want to lose and we didn't want to lose," Beltran said.
Pinch-hitter Daniel Descalso singled with one out in the 13th off Dodgers rookie pitcher Chris Withrow, then Matt Carpenter walked. Jansen, usually the Dodgers' closer, relieved and Beltran won it with his hit on a 3-1 count.
Winning pitcher Lance Lynn strengthened his case for a possible Game 4 start with two scoreless innings of relief. Withrow took the loss.
"There were a lot of big outs that both teams got tonight," Dodgers manager Don Mattingly said. "If the rest of the series is like this game, it should be a pretty good one."
The Dodgers had two runners on base in the ninth, 10th and 11th and still came up empty. They stranded 11 overall while going 1 for 10 with runners in scoring position.
Dodgers starter Zack Greinke struck out 10 in eight innings, allowing just four hits. Cardinals starter Joe Kelly left after the sixth with the score 2-2.
Mark Ellis tripled with one out in the Dodgers 10th. After an intentional walk, Michael Young followed with a fly ball to shallow right field that Beltran caught then made a strong, one-bounce throw to home plate where Ellis crashed into catcher Yadier Molina.
Molina held the ball, but it was hard to tell whether he actually tagged Ellis. On such plays, however, umpires almost always give the benefit to the catcher and called the runner out.
The Dodgers put runners at first and second with two outs in the 11th against John Axford. Pinch-hitter Nick Punto, who played for the Cardinals on their 2011 World Series championship team, struck out to end the inning.
Young got another chance in 12th. With runners on first and second, he grounded into an inning-ending double play against Lynn.
The teams are postseason foes for the first time since a Dodgers sweep in their 2009 division series. It's their first NLCS matchup since 1985, when the Cardinals won in six games.
Game 2 will feature a marquee pitching matchup; major league ERA leader Clayton Kershaw vs. Cardinals rookie Michael Wacha, who's flirted with no-hitters his past two starts.
Kershaw started the division series clincher against Atlanta on three days' rest Monday and will be on regular rest in Game 2.