Johnny Cueto spun a three-hit shutout to lead Cincinnati to a 5-0 victory in the opener of the twinbill, but Ross (5-3) returned the favor in the nightcap, holding the Reds to one run on three hits and five walks while striking out eight over seven strong frames.
Rivera sparked San Diego's offense with a two-run homer in the second, while Alonso added an RBI single in the sixth and a solo shot in the eighth to provide plenty of support for Ross.
Everth Cabrera also clubbed a solo homer for the Padres, who had won four straight before being blanked by the Reds in the twinbill opener.
Brandon Phillips plated the lone run for Cincinnati, which has lost five of its last eight games.
Reds starter Jeff Francis (0-1) was recalled from Triple-A Louisville prior to the game and allowed three runs on five hits over five innings in his first big league start of the season.