Shin-Soo Choo opened the Cincinnati fifth with a single and, two pitches later, Heisey pulled a pitch into the left-field seats for his first home run of the season and a 5-3 Reds lead.
That pinned the loss on Angels starter Joe Blanton (0-1), who was charged with all five (four earned) Cincinnati runs on seven hits. He walked one and struck out four.
Bronson Arroyo (1-0) got the win, scattering eight hits and three runs over six innings. He struck out five and also walked one. Aroldis Chapman pitched a one-hit, one-strikeout ninth for the save.
The Reds scored in the first and second innings with Choo hitting Blanton's first pitch of the day for a home run and Todd Frazier leading off the second with another homer.
An Albert Pujols sacrifice fly tied the score in the fifth before Heisey's two-run home run in the bottom of the inning.
Pujols got another RBI with a fielder's choice in the seventh.