Adrian Gonzalez added a late two-run single as the NL-leading Dodgers (66-50) thoroughly shut down their Southern California neighbors in Anaheim, allowing one run in two games to win the Freeway Series for the first time since 2006.
"It's just great to get wins against good teams like that," said Matt Kemp, who drove in a run and scored another. "It builds our confidence up to come in here and get two games in the way we did."
Ryu (13-5) was brilliant in his fourth victory in five starts, striking out four and allowing just two runners to reach third base. The Korean left-hander threw a shutout last year in his only previous start against the Angels.
"It just felt really good to do it again," Ryu said through a translator. "Last year, I had that really symbolic game for me. I just tried to duplicate the outcome. It's a great thing to be on a winning streak and to take the series here."
The Dodgers moved to a season-best 16 games over .500 and improved the majors' best road record to 36-23.
The Angels (67-47) managed just two runs on eight hits in the final 24 innings of the series, falling three games behind Oakland in the AL West and for the majors' overall best record.
David Freese's one-out double in the fifth was the first hit for the Angels, who were shut out for the third time all season. They have lost three straight for the first time in more than two months.
"There are going to be stretches where you're not pitching well and not playing well," catcher Chris Iannetta said. "We're not playing bad right now. We're just not playing to our potential. ... Hopefully we can tread water, hang in the race and not fall too far behind from Oakland."
C.J. Wilson (8-8) had another rough outing in his second start back from the disabled list. He yielded six hits and four walks in his fifth consecutive winless start, throwing just 54 of his 100 pitches for strikes.
The Dodgers led 3-0 in the third on Ramirez's bases-loaded single and Kemp's sacrifice fly.
Kemp scored on Juan Uribe's long double in the sixth. Kemp was ejected in the eighth after taking a called third strike with the bases loaded.
Mike Trout went 0 for 3 with a walk on his 23rd birthday. The ballpark was festooned with dozens of congratulatory signs from Angels fans.
The Angels briefly showed life when Albert Pujols' sixth-inning double ended an 0-for-20 combined skid by Trout, Pujols and Josh Hamilton. But Yasiel Puig sprinted and leaped to catch Hamilton's inning-ending drive at the warning track.
Dodgers: Josh Beckett is having an MRI exam after feeling pain in his hip while playing catch Wednesday. He will miss his scheduled start Friday.
Angels: Wilson is healthy enough to pitch, but his return from a sprained ankle hasn't gone smoothly. With Tyler Skaggs sidelined for the near future with a strained forearm, the Angels don't have many options to give Wilson more time.
Dodgers: Roberto Hernandez (6-8, 3.87 ERA) will start in Milwaukee one day after the Dodgers acquired him in a trade with Philadelphia.
Angels: Jered Weaver (12-6, 3.59 ERA), who hasn't lost since June 21, will open a series against the Boston Red Sox.