The Astros forged a 4-0 lead in the initial frame before a single out had been recorded.
Jonathan Villar, Jose Altuve and Jason Castro hit consecutive singles off Josh Johnson to begin the game, grabbing a quick 1-0 lead, and Carter followed by smacking the first pitch he saw over the center field fence for a three-run blast.
Matt Dominguez went 2-for-4 with a solo homer and two RBI and Justin Maxwell also went deep as Houston rebounded from a pair of losses to open the four-game series.
Dallas Keuchel (5-5) earned the decision despite allowing six runs on 10 hits over 7 1/3 innings and Jose Veras hurled the final 1 2/3 frames, notching his 19th save.
Johnson (1-7) absorbed his fifth loss in five starts, yielding seven runs on seven hits in a 5 2/3-inning effort.