Harang fell one strikeout short of the all-time major league record of 10 by Hall of Fame right-hander Tom Seaver of the New York Mets on April 22, 1970, also against the Padres.
Harang broke the 50-year-old Dodgers mark of eight consecutive strikeouts set by Johnny Podres against the Philadelphia Phillies on July 2, 1962.
Harang finished with 13 strikeouts in 6 1/3 innings and received a no-decision.
Harang, an 11-year veteran, was making just his second start for the Dodgers after they signed him last winter to a two-year, $12 million free-agent contract with an $8 million club option for 2014.
He struggled in his first start for the Dodgers against the Padres on Sunday at Petco Park, giving up four runs (three earned) on seven hits with five walks and lasting just 4 1/3 innings.
Harang spent last season with the Padres, going 14-7 with a 3.64 ERA.