Astros shortstop Carlos Correa drove in three runs in the victory at Minute Maid Park in Houston.
The win helped the Astros (16-13) snap a three-game losing streak. The Angels (9-21) now have the most losses in Major League Baseball.
Tucker gave the Astros a 1-0 lead with a leadoff home run in the bottom of the second inning. Reddick plated Yuli Gurriel in the same frame with an RBI single for a 2-0 edge. David Fletcher cut the Astros lead in half with an RBI single in the top of the third before the Astros responded with three runs.
Angels left fielder Justin Upton hit his third home run of the season in the top of the fourth inning to make the score 5-2. Anthony Rendon and Albert Pujols each hit RBI singles for the Angels in the fifth inning to cut the Astros lead to one run.
Correa responded with a three-run double in the bottom of the sixth to push Houston's advantage to 8-4. Tucker hit an RBI double in the next at-bat to plate Correa for the Astros' ninth run.
Astros outfielder Myles Straw hit a two-run double in the bottom of the seventh inning for the final two runs of the game.
Angels starter Patrick Sandoval allowed seven hits and five runs in 2 2/3 innings to move to 0-4 on the season. Fletcher went 3 for 5 with an RBI and a run scored for the Angels.
The Angels again face the Astros at 4:05 p.m. EDT Tuesday in Houston.