Richard (1-0) was sensational, keeping the Dodgers baffled with an assortment of off-speed pitches, which led to five strikeouts. He was touched for just five hits and two walks.
Kenta Maeda (0-1) pitched five innings, allowing three runs on six hits and two walks. He struck out four.
Richard was released last year by the Chicago Cubs after 25 relief appearances produced a 0-1 mark and a 6.43 ERA. He signed with the Padres in August and made nine starts, going 3-3 with a 2.41 ERA in his second stint with San Diego.
The Dodgers, fresh from scoring 14 runs on 14 hits in beating the Padres on Opening Day, didn't look like the same offensive club. With a mostly right-handed lineup to counter Richard, the Dodgers had little pop and did not get a runner to second base.
Richard has two career shutouts, the last one coming in 2012. But he was lifted after throwing 99 pitches Tuesday.
Solarte had an RBI single in the first and homered in the third off Maeda for a 3-0 lead. Wil Myers scored on Ryan Schimpf's sacrifice fly in the first inning and added an RBI single off reliever Ross Stripling in the eighth after Manuel Margot took third on catcher Yasmani Grandal's errant throw.
The Dodgers didn't have much luck against Richard, who wiggled out of trouble thanks to double plays in the first, second and fourth innings. Despite four hits and two walks, the Dodgers didn't have a runner reach scoring position.
NOTES: Padres RHP Carter Capps faced live hitters before the game. Capps, who started the season on the disabled list, missed last season after Tommy John surgery. He'll throw another side session before being deployed for a minor-league outing. ... Dodgers CF Joc Pederson, who had a grand slam and five RBIs in Monday's win, was out of the lineup with the left-handed Clayton Richard starting. Pederson, who will occasionally sit against lefties with plus off-speed pitches, was replaced by the right-hand-hitting Kike Hernandez. ... Dodgers LF Franklin Gutierrez was in the lineup for Andrew Toles in a preview of the team's platoon approach in left field. ... Former Dodgers great Pedro Guerrero is recovering in a New York hospital after suffering a stroke on Monday.