Lester (2-1) struck out eight in six shutout innings to outduel Haren as the visiting Red Sox beat the Angels, 4-3 — Boston's 11th triumph over the Angels in 12 games dating to last season.
J.D. Drew had two hits and a run batted in for Boston, and Jed Lowrie scored twice as Haren (4-1) lost for the first time in 13 starts before 39,005 at Anaheim Stadium.
The Angels closed within a run upon Lester's departure as Bobby Abreu drove in an eighth-inning run with a single, then scored from second base on a passed ball.
Red Sox closer Jonathan Papelbon stranded a runner at first in the ninth to claim his fifth save.
Haren retired the first seven Red Sox he faced, striking out three, before catcher Jarrod Saltalamacchia struck a towering fly ball toward the right-field wall that hit a jumping Torii Hunter's glove and fell to the warning track.
Hunter has proved capable of making that catch, so when the next batter, Marco Scutaro, flied out to him, all could see Hunter's disappointment at the missed catch transfer into a rifled throw to third base that beat Saltalamacchia to the bag.
Except base umpire Brian Gorman directed his gaze not on Alberto Callaspo's tag on Saltalamacchia's belly, but on the thumb guard that shot to foul territory. Angel Manager Mike Scioscia burst from the dugout to complain how Gorman could confuse the material with a baseball.
"Sometimes, you're not going to get the calls, and you have to play at a high level to absorb them," Scioscia said.
The mistake increased in significance when Jacoby Ellsbury singled to right, scoring Saltalamacchia.
An Angels' miscue grew the deficit to 3-0.
After a two-out walk and double in the fourth, slumping Red Sox free-agent pickup Carl Crawford skied a fly to shallow right-center that brought center fielder Peter Bourjos, Hunter and second baseman Howie Kendrick converging toward one another.
Bourjos had impressively run down an opposite-field liner by Adrian Gonzalez earlier, but this time there was confusion about the sinking fly among friends and Bourjos dropped the ball, allowing two runs to score.
"It's a little bit of inexperience in center field," Scioscia said. "As the center fielder, you're the captain. He thought Torii or Howie had it ... you don't give up on the ball early."
The Red Sox added a sixth-inning run and Haren then exited, unsuccessful in his attempt to join Weaver as the only teammates to start 5-0 in a team's first 20 games since it was done by a pair of Cleveland Indians (Stan Coveleski and Jim Bagby) in 1920.
"Weird game," Haren said. "There was a good chance I wasn't going to go 34-0."
Lester struck out the first four Angels he faced and only let one runner reach third base, a threat snuffed in the third when Abreu lined out to center.