The rookie hit a tiebreaking double during a three-run eighth inning and the Rays won their fourth straight game by beating the Toronto Blue Jays 4-2 on Saturday.
"I struck out twice tonight looking," Beckham said. "I wasn't too happy about that. I just wanted to get another AB and another opportunity to hit the ball hard."
James Loney got the Rays even at 2 with a pinch-hit RBI double before Beckham's hit off Miguel Castro gave Tampa Bay a 4-2 advantage.
"You always want to be part of it," said Loney, who homered in his return from an oblique injury in Friday night's 12-3 win over Toronto. "We just want to keep it going."
Ernesto Frieri (1-1) struck out all three batters he faced for the win. Brad Boxberger pitched the ninth for his fifth save.
Brett Cecil (1-2) faced one batter, giving up a two-out single to David DeJesus, who entered on defence in the top of the eighth when centre fielder Desmond Jennings exited with left knee soreness.
The Blue Jays have dropped two of the first three games in the series, and have won just one of their last 23 series at Tropicana Field.
"What are you going to do?" Toronto manager John Gibbons said. "It's on the schedule, you've got to play here. Play better."
Toronto rookie Daniel Norris allowed one run and five hits in seven innings on his 22nd birthday. The lefty struck out seven and walked three.
Russell Martin opened the seventh with an opposite-field homer to right off Steve Geltz that put the Blue Jays up 2-1.
Martin and outfielders Michael Saunders and Dalton Pompey were in the Toronto lineup, marking the first time in major league history that three Canadian position players started in the same game.
Blue Jays rookie Devon Travis went 2 for 4, extending his hitting streak to 11 games. He doubled in the first and scored on Josh Donaldson's single.
Tampa Bay tied it at 1 later in the first when Evan Longoria got the first of his four hits, a pop-fly double down the right-field line.
"There are guys top to bottom in the lineup coming through with big hits," Longoria said. "Really just never giving up."
The four hits by Longoria tied his career high.
Erasmo Ramirez, who entered with a 21.32 ERA in three games, gave up one run and four hits over four innings for Tampa Bay.
Blue Jays: OF Jose Bautista (shoulder) missed his fourth straight game and is day to day.
Rays: Jennings is day to day. ... Tampa Bay closer Jake McGee (back) threw a 21-pitch bullpen session and might pitch Tuesday for Class A Charlotte.
Tampa Bay purchased the contract of LHP Everett Teaford from Triple-A Durham and designated 1B Allan Dykstra for assignment.
Gibbons talked with the umpires following Beckham's hit after he was told by someone in the dugout that Rays third base coach Charlie Montoyo may have touched one of the baserunners.
"You're not allowed to do that," Gibbons said. "But you can't review that."
Tampa Bay RHP Chris Archer (2-2) expects no carry-over Sunday when he faces the Blue Jays for the first time since April 16, when Longoria was hit by a pitch one inning after Archer plunked Edwin Encarnacion.
"It seemed more like a misunderstanding than anything," Archer said. "I'm not going to try and throw 99 (mph) and hit somebody. That's just dangerous."
LHP Mark Buehrle (3-0) starts for Toronto.