The Angels (72-49) are alone in first place in the AL West for the first time since 2011, but they are only two percentage points ahead the Athletics, who lost at Atlanta on Saturday.
''We haven't accomplished anything yet,'' Pujols said. ''Let's not get too far ahead of ourselves. When we accomplish our goal, then we can talk about it.''
With his team in fifth place, Rangers manager Ron Washington talked about the division race.
''I think it's going to come down to who continues to pitch well,'' he said.
The Angels finished 78-84 and in third place during an injury-plagued 2013 season.
''It definitely feels good to be on the track we hoped to be on last year,'' manager Mike Scioscia said.
One reason for their improvement to the best record in the major leagues is a better bullpen.
Huston Street worked a scoreless ninth inning for his 33rd save in 34 opportunities. It was the second straight night the Rangers rallied before losing 5-4.
Los Angeles has won nine in a row over Texas, tying the series record set during the 1985 season and matched a year later.
Street hasn't allowed a run in 12 games with the Angels since being acquired from San Diego on July 18.
''He's just a bona fide closer,'' Scioscia said. ''He has created an opportunity for us to shorten the game by moving (Kevin) Jepsen up to the seventh inning, and Joe Smith up to the eighth.''
Angels starter Matt Shoemaker (11-4) pitched three perfect innings before Shin-Soo Choo led off the fourth with a home run, but by that time, the Angels led 5-0.
Kendrick added two singles in a 3-for-4 night. Kole Calhoun had a single and a double for the Angels, and Erick Aybar had two singles.
Pujols hit a solo homer in the first against starter Colby Lewis (8-10). Kendrick hit another solo shot in the second.
Los Angeles' Chris Iannetta doubled home another run in the second, and Calhoun singled to drive in two more in the fourth. Both hits, like Pujols' homer, were with two out.
Angels: Los Angeles activated RHP Mike Morin (left foot laceration) from the disabled list. He pitched an inning in relief.
Rangers: Rios made his fourth consecutive start after aggravating a sprained right ankle on Aug. 10. RHP Yu Darvish (inflamed elbow) won't travel with the team to Miami on Monday, and will continue treatment in Arlington.
The teams' three-game series concludes on Sunday. Angels LHP Hector Santiago (3-7, 5.84) defeated the Rangers 15-6 on July 10 in Arlington. Texas RHP Nick Tepesch (4-7, 4.29) last faced the Angels on July 11, when he lost 3-0.
Rangers 1B J.P. Arencibia had been 0-for-19 before his run-scoring single in the fourth. RF Alex Rios was 0-for-16 before his two-run single in the seventh. LF Jim Adduci went 0-for-4, and is in an 0-for-20 slide. Angels CF Mike Trout went 0 for 5, extending his skid to 0 for 15.
HOT HOT HOT
Calhoun stretched his hitting streak to a season-high seven games. In six of those games, he has had multiple hits. He is batting .441 (15-for-34) during the streak. Calhoun has five RBIs in the series' first two games.
Texas CF Leonys Martin is 10-for-20 (.500) in his last five games, including two singles on Saturday.
Lewis struck out 10 batters for the first time since June 17, 2012. The 10-year veteran's career high is 12, posted May 10, 2012.
Kendrick's home run was his ninth in Arlington - the most he has hit in any road ballpark.