The win gave New York a 4-2 victory in the best-of-seven ALCS and lifted them into the Fall Classic for the first time in six years.
Andy Pettitte pitched into the seventh for the win, a 16th career postseason victory that put him on top of MLB's all-time list. He was aided by a two-run single from Johnny Damon in New York's three-run rally in the third that erased a 1-0 deficit.
Pitcher CC Sabathia, who won two games in the series, was named MVP.
The Yankees, winners of a record 26 Major League Baseball championships, will host the Phillies in the opening game of the best-of-seven World Series Wednesday.
"This is a great time," Yankees manager Joe Girardi told reporters under a spray of champagne in the team's clubhouse. "But we're not done yet."
Second baseman Robinson Cano led a group of team-mates back on the field to spray champagne on some of the fans among a record crowd of more than 50,000 at the new Yankee Stadium.
Los Angeles scored a run off Yankee closer Mariano Rivera in the top of the eighth to claw their way to 3-2, but sloppy fielding allowed some breathing room for New York.
The Bronx Bombers added two runs in the bottom of the eighth without benefit of a hit thanks to Angels miscues on two sacrifice bunts. Second baseman Howie Kendrick dropped a throw covering first to allow Nick Swisher to reach base after a walk to Cano.
New York's fourth run of the game scored when Scott Kazmir lobbed a throw to first well over Kendrick's head on Melky Cabrera's sacrifice bunt, and Cano came around to score. Mark Teixeira stroked a sacrifice fly to bring home the last run.
