Tillman gave up two runs and four hits over seven innings, and tied a career high in striking out nine, while Nick Markakis, Adam Jones, Manny Machado and Matt Wieters posted RBI for the Orioles, who moved within 1.5 games of the idle Tampa Bay Rays.
Alex Rodriguez and Lyle Overbay connected for the Yankees, in a game which also featured a first-inning bust-up between rival managers Buck Showalter and Joe Girardi.
Like Baltimore, Cleveland also boosted their AL wild-card hopes - with a 4-3 win against the Kansas City Royals. Ubaldo Jimenez struck out 10 in seven innings, while Asdrubal Cabrera, Yan Gomes and Carlos Santana all hit solo homers for the Indians.
In other American League action, Chris Sale allowed just four hits over eight innings, striking out eight for the Chicago White Sox in their 5-1 victory over the Detroit Tigers at US Cellular Field, and the Houston Astros were 6-4 winners against the Seattle Mariners.
The Pittsburgh Pirates secured their first winning season in more than two decades by toppling the Texas Rangers 1-0 in interleague play, Pedro Alvarez driving in the game's lone run with a two-out double in the seventh inning.
In the National League, a five-run fourth-inning rally helped Atlanta end a four-game skid with a 5-2 victory over the Miami Marlins. Kris Medlen pitched 6 1/3 strong innings for the Braves.
Ryan Sweeney and Luis Valbuena had solo home runs in the Chicago Cubs' 2-0 success against Cincinnati. Travis Wood struck out seven and allowed six hits in seven innings for a first career win over the Reds.
Gio Gonzalez tossed a one-hit shutout as the Washington Nationals posted a third straight triumph with a 9-0 rout of the New York Mets, the Los Angeles Dodgers trounced the Arizona Diamondbacks 8-1 and the San Francisco Giants edged the Colorado Rockies 3-2 in 10 innings.