The Angels had scored a total of just two runs in their previous three games, including a 3-0 loss to the Indians a night earlier.
Anderson homered off C.C. Sabathia (2-2) in the first inning, and Paul broke a 2-all tie in the fifth with his first extra-base hit of the season.
"I think Garret got us going. For him to step up and hit that home run, I think we all just went, `Whew. OK, let's go back to work,"' Paul said.
Vladimir Guerrero doubled and singled twice in Los Angeles' 11-hit attack.
"We had some missed signals on the bases, some of our game went by the wayside, but our hitting picked up," Angels manager Mike Scioscia said.
Asked if Anderson's early two-run homer came at a good time, Scioscia smiled and said, "The way things were going, we'd take two anytime."
The Angels' Paul Byrd (3-3) gave up three runs and eight hits in six innings. Scot Shields pitched two perfect innings, striking out the side in the eighth, and Rodriguez came on to earn his ninth save in 10 chances.
"The fact that our offense came alive is important," Byrd said. "When Josh Paul came up and hit a two-run homer, it was huge. He doesn't get a chance to play very much."
Sabathia allowed four runs and eight hits in 6 1/3 innings. He struck out five and walked one.
"I was kind of all over the place early," Sabathia said. "I really couldn't spot the ball well and couldn't command the ball the way I wanted to, but I felt like I battled.
"I'm very encouraged by the way I handled the situation after giving up two runs in the first inning. Last year, or in years past, I probably wouldn't have made it out of the third inning."
In the Angels' fifth, Orlando Cabrera drew a leadoff walk and stole second. Paul, 2-for-17 coming into the game, came up two outs later and drove a 2-2 pitch from Sabathia over the wall in left-center.
Cleveland narrowed the gap to 4-3 in the sixth, when Crisp doubled with two outs and scored on Grady Sizemore's triple to right-center field.
Peralta hit a solo homer off Byrd in the third to pull the Indians within 2-1. The homer was his third.
Cleveland manager Eric Wedge is still looking for offensive consistency from the Indians.
"We hit the ball hard tonight and made a lot of hard outs. I thought our at-bats were a little bit better, but we're still just not finishing things off," Wedge said.
"To be a more consistent winning team, we've got to finish things off. We're making it awfully hard on ourselves."
- Crisp's homer was his third of the year and second in as many nights.
- Cleveland C Victor Martinez, who had thrown out only five of 25 runners attempting to steal this year, threw out two in quick succession in the second inning. Cabrera singled and Martinez made a perfect throw to second to easily cut him down, then Steve Finley singled and tried to steal and the Indians' catcher made another good throw to get Finley and end the inning. Martinez also picked Guerrero off second in the eighth.