Chacin (11-6) scattered five hits, walked two and struck out six, lowering his ERA to 3.13 in posting his seventh straight start of allowing three or fewer earned runs.
The Rockies supported him with a season-high 14 runs en route to their first four-game winning streak since April.
Fowler led the way, going 3-for-4, including a two-run single in the fifth and a two-run double to cap a six-run uprising in the eighth.
Wilin Rosario contributed three RBI, Nelson Arenado went 4-for-5 with a run-scoring single and DJ LeMahieu added three hits, including a solo homer, and scored three times as Colorado rolled to a win the opener of a three-game set.
Padres starter Edinson Volquez (8-10) was pounded for eight runs on nine hits over just 4 1/3 innings.
Jedd Gyorko went 2-for-4 with a bases-empty clout for San Diego.