ST. LOUIS — Gerrit Cole gave up two hits in six dominant innings and had an RBI in his playoff debut as the Pittsburgh Pirates beat the St. Louis Cardinals 7-1 Friday to even their National League division series at a game apiece.

The Atlanta Braves also evened their NL division series with Los Angeles at a game apiece after beating the Angels at home 4-3.

In the American League, the Boston Red Sox took advantage of poor Tampa Bay defense in a five-run fourth to beat the Rays 12-2 in Game 1 of their division series and the Detroit Tigers held on to beat the Oakland Athletics 3-2 in their series-opening game.

The Pirates showed poise in their first playoff win since 1992 and St. Louis looking tentative in the field — a role reversal from the Cardinals' 9-1 win in the opener against Pittsburgh.

Cardinals starter Lance Lynn, who hasn't lasted long enough to qualify for the victory in any of his three career playoff starts, yielded five runs and seven hits in 4 1-3 innings.

Cole, meanwhile, struck out five batters and walked one. After allowing Carlos Beltran's double with one out in the first, he retired 11 straight before Yadier Molina led off the fifth with his third career postseason homer.

"I just trusted myself and tried to keep it as simple as I could," he said. "You just try and clear you mind after every pitch and just look forward."

Pedro Alvarez homered for the second straight game for the Pirates, who host Game 3 today.

In Atlanta, Mike Minor pitched six strong innings, Jason Heyward had a two-run single and the Braves pulled off some nifty plays in the field to hold off the Dodgers.

In a postseason already marked by numerous defensive miscues, including some shaky plays by the Braves in Game 1, Atlanta's defense came through by turning three double plays — none more crucial than the one Luis Avilan started in the seventh to escape the inning with a 2-1 lead intact.

Hanley Ramirez drove in all three runs for the Dodgers, including a two-run homer in the eighth.

Not taking any chances, the Braves went to closer Craig Kimbrel for a rare four-out save. He ended the eighth by retiring Juan Uribe on a groundout, then pitched around two walks in the ninth.

The best-of-five series shifts to Los Angeles today.

Jon Lester gave up a pair of solo homers to Tampa Bay, but Boston got the lead back when the Rays fell apart in the fourth. One ball fell between two outfielders, one batter reached safely on a dropped third strike and another reached when pitcher Matt Moore was slow to cover first.

By the time it was over, the Red Sox were ahead 5-2 and on their way to the early lead in their AL division series.

The Red Sox added three more runs to chase Moore in the fifth inning, when they sent nine batters to the plate — the first time in franchise history they have batted around in consecutive innings in a postseason game.

In all, Moore was charged with eight runs — seven earned — on eight hits, two walks a hit batter and a wild pitch, striking out four in 4 1-3 innings.

Every Boston starter got a hit and scored a run, the first time a team had done that in the Major League Baseball postseason since Lou Gehrig, Joe DiMaggio and the Yankees in the 1936 World Series.

In Oakland, California, Max Scherzer struck out 11 over seven dominant innings to help give Detroit a 1-0 lead in their AL division series rematch.

Scherzer retired 16 of his first 18 batters and was nearly untouchable before Yoenis Cespedes hit a two-run drive in the seventh for his first career playoff home run. The strikeouts were his most in seven postseason starts.

Major League Baseball's lone 20-game winner, Scherzer (21-3) allowed three hits and walked two.

Miguel Cabrera and Alex Avila each hit first-inning RBI singles against 40-year-old MLB All-Star Bartolo Colon, whose winless streak against the Tigers extended to 10 and a half years.