Tyler Cloyd (1-0) allowed two runs and eight hits in seven innings. He was recalled from Triple-A Lehigh Valley (International League) earlier in the day.
Miami's Jose Fernandez went five innings, allowing one run and five hits. He walked one and struck out two.
Philadelphia went ahead 2-1 in the sixth when Domonic Brown's ground out scored Howard from third. Howard led off with a single and took third on Young's double to deep center off Duane Below (0-1).
Howard's single with the bases loaded scored two runs and highlighted a four-run seventh that gave the Phillies a 6-1 lead. Howard returned to the lineup after missing two games with a sore left knee. He received a cortisone shot Sunday.
Young's ground out and Brown's double scored the other Phillies runs in the seventh. Young homered to left-center on a 2-2 pitch with one out in the fourth. It was his second home run of the season.
Juan Pierre's seventh-inning RBI single pulled Miami within 6-2.
Howard added an RBI single in the eighth off Wade LeBlanc.
Miami's Justin Ruggiano had a run-scoring double with two outs in the ninth.
Pinch-hitter Jordan Brown's sacrifice fly in the fifth scored Placido Polanco to tie it at 1 and take Fernandez off the hook.