Darvish allowed four runs on seven hits and a walk, striking out six to help the American League West-leading Rangers improve to 27-14 - the best record in the Major Leagues.
Will Middlebrooks belted a go-ahead three-run double off Fernando Rodney in the ninth inning to hand the Boston Red Sox a come-from-behind 4-3 triumph over the Tampa Bay Rays.
The AL East-leading New York Yankees slumped to a second straight loss, going down 3-2 against Seattle. Hector Noesi pitched into the fifth inning for the Mariners, giving up an unearned run and three hits.
Also in the American League, the Chicago White Sox edged the Los Angeles Angels 5-4.
In the National League, Home runs from Bryce Harper and Adam LaRoche lifted Washington to a 6-2 success against the San Diego Padres.
Stephen Strasburg threw down eight solid innings for the Nationals at Petco Park, allowing two runs on three hits.
NL RBI leader Brandon Phillips drove in two runs as the Cincinnati Reds earned their sixth consecutive win - a 5-3 triumph over the Miami Marlins.
Daniel Murphy doubled twice as the New York Mets snapped a six-game losing streak by defeating the St Louis Cardinals 5-2.
Finally, Travis Snider drove in three runs as the Pittsburgh Pirates thrashed the Milwaukee Brewers 7-1 and the San Francisco Giants rallied from a six-run deficit to sink the Colorado Rockies 8-6.