Haren (1-1) pitched eight strong innings, Torii Hunter hit a solo homer and Pujols singled during a first-inning rally after a cold drizzle delayed the start of the game 147 minutes.
"I just hopes this sparks us," Haren said after the Angels won for only the third time in 11 games. Los Angeles remained last in the AL West and still mired in a slump that includes Pujols' longest homerless drought of his career.
Pujols hasn't hit a home run in an Angels uniform, a streak of 21 games and 84 at-bats. He has not connected since Sept. 22, an overall stretch of 113 at-bats, and remains stuck at 445 career homers.
The first baseman did hit five homers in the 2011 postseason, including three in the World Series, to help the St. Louis Cardinals win it all. He then signed a $240 million, 10-year contract as a free agent with the Angels.
"I think he's going to hit a home run sometime," Angels manager Mike Scioscia said. "If it reaches something like 300 at-bats, then we'll have a different conversation. In the meantime, he got a big hit in that inning."
Scioscia believes moving to the AL may have something to do with Pujols' prolonged power funk.
"You never know when a guy crosses leagues," Scioscia said. "It could have something to do with it. He's gotten into some poor counts, but he'll figure it out."
Indians manager Manny Acta agreed.
"Switching leagues plays a role," Acta said. "There's nothing like familiarity with pitchers. He's going to be OK -- hopefully right after (they leave) Sunday."
In the Angels' first inning, Howard Kendrick drew a one-out walk, took third on Pujols' hit and scored on a single by Kendrys Morales that bounced just beyond the reach of two infielders for a 1-0 lead against Jeanmar Gomez (1-1).
Hunter's homer in the fourth made it 2-0. The Angels have hit only five homers in their last 104 innings.
Haren made the lead stand up. The right-hander allowed four hits and struck out seven.
"That was important, how he kind of served as his own setup man," Scioscia said. "He had a good fastball on both sides of the plate. Early on, he had some great splits."
Haren got three quick outs in the first inning after Michael Brantley hit a leadoff double. Rookie outfielder Mike Trout, called up Friday night when veteran Bobby Abreu was released, tried to make a diving catch of the slicing drive near the left-field line.
"That first play showed he was a little amped up," Scioscia said of Trout's earnest if ill-fated effort.
Brantley said Haren quickly settled into a rhythm.
"He does what he always does," Brantley said. "He keeps you off-balance. He throws all his pitches for strikes. He throws what looks like a good strike and it ends up as a ball. He's a good pitcher."
Jack Hannahan's two-out RBI single got Cleveland within 2-1 in the fourth.
Scott Downs worked a perfect ninth for his first save.
"Having Scott close it out was important," Scioscia said.
It was only Downs' second save in the last three seasons and the Angels' second in eight chances this year as Los Angeles improved to 1-6 in one-run games.
The left-hander was moved from pitching setup and into the closer's role in place of young right-hander Jordan Walden on Friday.
Meanwhile, the Indians' team-wide power drought continued. They haven't homered in 10 games, a streak of 93 innings and 334 at-bats -- their longest in nearly 30 years. Cleveland went 14 games without a homer from April 10-22, 1983.
"We hit one in nine games in a row," Acta said. "That's how the game goes. It evens out. We're going to hit another one, believe me. When you have such a long season, everything comes in cycles."
Gomez struck out a career-high seven over six innings. The right-hander gave up five hits, two runs and two walks.
Angels RHP Ervin Santana is scheduled to start Sunday -- his first appearance against Cleveland since pitching a no-hitter at Progressive Field on July 27. ... Cleveland has 99 walks, most in the majors. ... Hunter's homer left him four runs shy of 1,000 for his career. ... Pujols needs two runs for 1,300. ... The Angels have used 19 different lineups in 21 games. ... The poor weather kept Indians OF Shin-Soo Choo from testing his strained left hamstring in pregame workouts. Choo has not played since the eighth inning Tuesday. ... Cleveland dropped to 6-1 in one-run games. ... The Angels had lost 11 straight one-game decisions since beating the New York Yankees 2-1 on Sept. 9.