Sosa's two-run homer in the seventh off Carlos Silva was his 584th, moving him past Mark McGwire and into sole possession of sixth place on the career list, two behind Frank Robinson.
Palmeiro went 3-for-5 to tie Al Kaline for 24th on the career list with 3,007 hits, and Tejada's first homer in a month lifted the Orioles to a 3-2 victory over the Minnesota Twins on Monday night.
Sosa and Tejada had both gone homerless since the same game on June 18. Sosa had not homered in 78 at-bats since connecting off Colorado's Byung-Hyun Kim, and Tejada, the All-Star MVP, went 95 at-bats without a homer before connecting on a 1-2 slider from Juan Rincon (1-2) to break a 2-all tie.
It was Tejada's 20th home run of the season.
"Right before he got up I said to him, 'Miggy this is your time of the game,'" Baltimore manager Lee Mazzilli said. "He's done that many times before."
Mazzilli's faith was justified when Rincon hung the slider, and Tejada pounced on it, driving it well into the seats in left field.
"When your manager says that to you, you get a lot more confidence," Tejada said. "I didn't try to hit a homer, I just wanted to get a hit."
Bedard, in his first start since May 21, allowed four hits in six shutout innings and struck out seven. Bedard, who went on the disabled list on May 22 with a sprained left knee, was activated before the game.
The Canadian lefty shut down the Twins through six innings, giving up just four runs while striking out seven.
"It's been a long time, pretty much two months, so to get back in the game and help the team get a win is a plus," Bedard said.
Twins starter Silva was equally impressive, making just the one mistake to Sosa in nine innings of work. He needed just 85 pitches in the outing, allowing eight hits.
Sosa ripped a monstrous 421-foot homer off Silva in the seventh to pass his friend McGwire. He gave his trademark hop out of the batter's box and rounded the bases for the 10th time this season and a 2-0 lead.
"I'm real happy to see him get that homer," Tejada said.
Sosa was not available for comment after the game.
Minnesota, which has lost eight of 11, rallied, but still managed to fall 13 games behind the White Sox in the AL Central and a half-game behind Baltimore in the wild-card race. Baltimore is tied with Boston for the wild-card lead.
Luis Rodriguez hit an RBI single off Jason Grimsley in the seventh to make the score 2-1.
Torii Hunter led off the ninth with a double into the corner off closer B.J. Ryan. Bret Boone followed with a bunt single, and Hunter raced around and scored to tie the game after Ryan dropped the throw from Palmeiro at first.
Hunter had a chance to win it against Jorge Julio (3-2) with runners on first and second and two outs in the 10th but struck out for the fourth time of the game.
"It's sad to be talking about our pitchers giving up three runs and losing a game," said manager Ron Gardenhire, who was ejected for arguing balls and strikes and viciously ripped home plate umpire Hunter Wendelstedt after the game. "Execution is everything in these close games and we're not getting it done."
- The Twins recognized Palmeiro for joining the 3,000-hit club Friday. The fans gave him a standing ovation and Palmeiro obliged with a tip of the cap.
- Hunter argued with Wendelstedt after being called out on strikes in the fourth. Hunter tried to check his swing, but Wendelstedt ruled he went around.
- The Orioles designated RHP James Baldwin for assignment to make room for Bedard.