The Reds jumped off to an 8-2 lead after 1 1/2 innings, but then quickly fell behind 9-8 as starter Mat Latos blew the big lead.
Cincinnati rebounded in the fifth on Ryan Ludwick's score-tying solo shot, then took the lead in the next frame when Joey Votto (4-for-4, two-run homer) collected a two-out single off Fernando Rodriguez (1-6) and came home on Phillips' double.
The Reds second baseman added a two-run single for some insurance in the eighth as the National League Central-leading Reds clinched their three-game set at Minute Maid Park.
Stubbs went 3-for-5 with a three-run homer and an RBI double in the victory.
Sam LeCure (1-1) tossed two scoreless frames to earn the win and Aroldis Chapman notched his fifth save for the Reds.
J.D. Martinez drove in three runs, Jose Altuve went 3-for-5 with three runs scored and Jed Lowrie bashed a two-run homer for Houston.