With the teams tied at 2, Randy Choate and rookie Seth Maness combined for a scoreless seventh inning and rookie Carlos Martinez handled the eighth. Rosenthal preserved the tie in the ninth and 10th (with a big assist from Beltran, the Cards' right fielder), newcomer John Axford worked out of a jam in the 11th, and Lynn finished things in the 12th and 13th.
"I believe that confidence and success breeds more confidence and success, and hopefully the guys will feel good about their chances of getting the job done, because we're going to throw them back in there," said Cardinals manager Mike Matheny.
"We trust them in big situations. The only way you can feel good about those is to be in them and have some success. Once again, we're exposing some of these kids to things that they haven't been exposed to before, and they keep doing the job. So we just enjoy throwing them back out there."
Matheny won't have to wait long. Game 2 of the series is scheduled for Saturday afternoon at 3 p.m. CT on TBS.
The Cards won by holding Dodgers hitters to 1-for-10 with runners in scoring position, with only three of those at-bats coming against a reliever.
"Everyone just did what they've been doing all season," said Axford, the Cardinals' most recent bullpen addition. "That's a good thing in the postseason."
It is not a new thing for St. Louis to feature solid relief in the postseason, but this is a different collection of arms. Maness, Martinez, Miller, Rosenthal and left-hander Kevin Siegrist all began the season with rookie status.
"We've got some good arms, young arms," catcher Yadier Molina said. "In 2006 and '11 [the Cards' most recent World Series appearances], we had some more veteran guys over there. But right now we have some young arms.
"It's different, but at the same time, it's fun. I hope this gives them confidence."
The Dodgers did have chances late in the game, with Martinez, Rosenthal, Axford and Lynn each allowing at least a hit or a walk. In the eighth, Martinez pumped his fist in celebration after inducing a big double play from the Dodgers' Juan Uribe, whose two-run single five innings earlier had briefly given the visitors a 2-0 lead. Axford was similarly emphatic after striking out pinch-hitter Nick Punto to strand a pair of runners in the 11th.
But the greatest escape belonged to Rosenthal. The rookie closer breezed through a 1-2-3 ninth inning but found trouble in the 10th when Mark Ellis' one-out triple skipped past Cardinals center fielder Jon Jay. Rosenthal intentionally walked Hanley Ramirez to face Michael Young, who hit a medium-depth fly ball to right-center field, where Beltran made the catch and fired home to complete an inning-ending double play.
When Molina held onto the baseball after a collision with Ellis, the inning was over.
"I was going to give those guys credit," Dodgers manager Don Mattingly said. "I mean we're down to the final four, and you're looking at two pretty good teams. And [we] played a pretty good game tonight with a lot of good pitching. There were a lot of big outs that both teams got tonight. Our pitching was really good. Theirs was good.
"We had a couple opportunities to get a run in, and we didn't do it. If the rest of the series is like this game, it should be a pretty good one."
Lynn threw 29 pitches and remains an option to start Game 4 of the series at Dodger Stadium on Tuesday (7 p.m. CT on TBS). Shelby Miller, who like Lynn warmed up earlier in the game while St. Louis starter Joe Kelly was grinding through six innings, is Matheny's other option. The Cards have not officially named a starter beyond Adam Wainwright in Game 3.
Martinez -- at 22, the youngest man to pitch on Friday night -- offered a veteran sentiment as players hustled home for a short night's sleep.
"Winning the first one is always important, and I feel fortunate to be able to do my part," he said. "This is a close series, so it's going to take all of us to win. We have a lot more to do here."