Until 1969, there was only one series played after the regular season and that was the World Series. Then they had the League Championship series which was played in a best-of-5 series from 1969-1984. In 1995, the Division Series started and that has been a best-of-5 series from the beginning. In 1981, there was both a 5-game Division Series and League Championship Series due to mid-season strike.
The Dodgers have played in 12 five-game series since 1974 (not counting their current series against the Atlanta Braves), and they are 5-0 after winning Game 1. Here's a look at how they have done after Game 1:
1974: The Dodgers played their first League Championship series against Pittsburgh and opened that series with a 3-0 shutout by Don Sutton (who faced future Dodger pitcher Jerry Reuss). They also won Game 2 to take a 2-0 lead. After losing Game 3 at home, the Dodgers and Don Sutton would win Game 4 and the series 3-1. Box Scores.
1977: In their first of three best of 5 series against the Phillies, the Dodgers would lose the first game at Dodger Stadium. After winning Game 2, the Dodgers won Game 3 in Philadelphia on a memorable ninth inning rally and then Tommy John pitched them to the pennant to win the series 3-1. Box Scores.
1978: In the their second series against the Phillies, the Dodgers on the back of four home runs, including two by Steve Garvey, won Game 1 in Philadelphia. The Dodgers would take Game 2 to come back to Dodger Stadium with a chance to wrap it up in three games. But they lost Game 3 which led to a walk-off pennant-clinching hit by Bill Russell driving home Ron Cey. Box Scores.
1981: The 1981 post-season would see the only time two best of five series would played to determine the pennant winner. This season had the first Division Series where the Dodgers would go on the road to play Houston. Houston not only won Game 1, they won Game 2 to need only a win in LA to move on. But like they did in 1980, the Dodgers would sweep the Astros over the weekend to win the series 3-2 (this would be the only time after falling behind 2-0, the Dodgers would win a best of 5 series). Box Scores.
Next up was the Montreal Expos, the Dodgers won Game 1, 5-1 behind home runs by Pedro Guerrero and Mike Scioscia but Ray Burris beat Fernando Valenzuela 3-0 to take the series back to Montreal tied 1-1. The Dodgers would fall behind 2-1 before winning Games 4 and 5, the pennant winner being a solo shot by Rick Monday on Monday afternoon. Box Scores.
1983: The Dodgers lost Game 1 to the Phillies 1-0 as Steve Carlton bested Jerry Reuss. The Dodgers would win Game 2 but then lost a pair of 7-2 decisions to the Phillies as they lost their League Championship series (and the last one they played as a best-of-5). Box Scores.
1996: Returning to the Division Series, this time as the Wild Card team, the Dodgers would find their experience similar to 1995 as they lost Game 1 to the Atlanta Braves 2-1 in 10 innings. The Braves would win the next two games albeit one of them being another one-run win but nonetheless the Dodgers were swept out for the second year in a row. Box Scores.
2004: If there was one thing you learn reviewing these playoff series, having an elite starting pitcher to pitch Game 1 is a nice thing to have, in 2004, Odalis Perez didn't make it out of the 3rd inning, giving up six runs and the Dodgers would lose Game 1 and then Game 2 in St. Louis. Despite the efforts of Jose Lima and Shawn Green who both led the Dodgers to a win in Game 3, the Cardinals won the next game to close out the series 3-1. Box Scores.
2006: The Dodgers would play the New York Mets in the post-season for the first time in 18 years but it would not be as memorable as the last time, the Mets made the biggest play of the series -- a double play at the plate as two runners were tagged out off the same throw. The Dodgers would lose that game 6-5 and soon the series as the Mets swept the Dodgers. Box Scores.
2008: The Dodgers had not won the first game of a 5-game series since 1981 and falling behind early to the Chicago Cubs, who had the National League's best record didn't seem like a recipe to fix that. But then James Loney hit a grand slam that gave the Dodgers the lead and the Dodgers never trailed again in this series. James Loney would get another key hit and Hiroki Kuroda would pitch the Dodgers to a sweep and they won first post-season series since the 1988 World Series. Box Scores.
2009: Matt Kemp hit a first inning home run off Chris Carpenter that gave the Dodgers the lead but how many remember this was a bullpen game as Randy Wolf left after 3⅔ innings, Jeff Weaver (who got the win), Ronald Belisario, Hung-Chih Kuo, George Sherrill and Jonathan Broxton pitched the remainder, giving up just one run and the Dodgers won 5-3. A dramatic walk-off win in Game 2 set up a somewhat anti-climatic win at St. Louis that completed the sweep. Box Scores.