ANAHEIM, Calif. — Eric Hosmer hit a two-run homer in the 11th inning, and the surprising Kansas City Royals took a 2-0 lead in the AL Division Series with a 4-1 victory over the Los Angeles Angels on Friday night.

Alex Gordon had an early run-scoring single and Salvador Perez added an RBI infield single in the 11th for the Royals, who became the first team in major league history to win three straight extra-inning playoff games.

In its first postseason appearance since 1985, Kansas City’s playoff roll just can’t be slowed by the majors’ best regular-season team. Hosmer had three hits and scored two runs as the Royals moved to the brink of the AL Championship Series.

Game 3 in the best-of-five series is Sunday in Kansas City, where Angels left-hander C.J. Wilson faces James Shields.

After 10 innings of intense, pitching-dominated baseball, the Royals broke out. Lorenzo Cain beat out a one-out infield single off losing pitcher Kevin Jepsen, and Hosmer smacked a no-doubt homer to right field, setting off a celebration for several dozen blue-clad fans in a sea of red at the Big A.

Albert Pujols had a tying RBI single in the sixth for the Angels, but the majors’ most productive offense has been mostly helpless against the Royals. Los Angeles, which led the big leagues with 98 wins, has just 10 hits and three runs in 22 innings.

Mike Trout got a chance to help in the 11th after second baseman Omar Infante made a throwing error on Kole Calhoun’s two-out grounder. But the AL MVP favorite struck out against Greg Holland, finishing his second straight 0-for-4 night in his first playoff series.

Only two teams since 1995 have rallied to win a division series after losing the first two games at home.

Kansas City’s cardiac kids have put an unlikely charge into October. The Royals are the first team to play in three consecutive extra-inning playoff games since the 1980 NLCS between Houston and Philadelphia, which had four straight.

They followed up their 12-inning wild-card victory over Oakland with a series-opening win on Mike Moustakas’ 11th-inning homer, and Hosmer kept it going with his decisive homer one night later.

Brandon Finnegan pitched a hitless 10th for the Royals, and the 21-year-old rookie earned the win. Greg Holland worked the 11th for his second save of the series.

In a matchup of impressive rookie starters, Yordano Ventura pitched five-hit ball for the Royals, and Matt Shoemaker threw six innings of five-hit ball for Los Angeles.

Ventura’s fastball was clocked at 102 mph in the second inning, and he was still hitting triple digits in the seventh. He escaped jams twice in the late innings, stranding three runners.

Shoemaker also was sharp in his playoff debut after a breakthrough 16-win regular season. The Angels’ 28-year-old rookie had six strikeouts while pitching for the first time since straining an oblique muscle on Sept. 15.

The Royals took an early lead for the second straight night when Hosmer singled, advanced on Calhoun’s error in right field and scored on Gordon’s single in the second inning.

After Ventura retired 10 straight in the early innings, the Angels evened it in the sixth with a two-out rally. After Calhoun singled and Trout walked, Pujols drove a 100 mph fastball to right for the first hit of his first postseason with Los Angeles.

Royals catcher Salvador Perez was hit in the head by Josh Hamilton’s backswing in the fifth inning. Perez, the hero of Kansas City’s wild-card playoff victory over Oakland, stayed in the game after a long moment on the ground.