A lead-off walk to Gregor Blanco in the seventh was the only stain on Bailey's night as he struck out nine in 109 pitches and threw the first no-no in the majors since his own effort against Pittsburgh in September.
Joey Votto scored Shin-Soo Choo on a sacrifice fly in the first to give Bailey all the run support he would need, before Brandon Phillips' two-run shot in the sixth padded the lead.
Clayton Kershaw also threw a complete-game shut-out to lift the Los Angeles Dodgers to an 8-0 victory over the Colorado Rockies.
Kershaw scattered four hits and fanned eight without walking a batter, while Adrian Gonzalez went yard and rookie Yasiel Puig homered once again.
The Rockies' Michael Cuddyer saw his hit streak end at 27 games.
David Price announced his return from the DL by striking out 10 in seven shut-out frames as the Tampa Bay Rays saw off the Houston Astros 8-0.
Desmond Jennings drove in four runs on three hits including a homer.
John Lackey tossed eight frames of one-run ball as the Boston Red Sox beat the San Diego Padres 4-1.
Brandon Snyder's three-run double in the fourth proved to be the key hit for the Sox, while David Ortiz secured the 500th double of his career.
Kendrys Morales had two home runs and six RBIs as the Seattle Mariners saw off the Texas Rangers 9-2.
Patrick Corbin suffered his first loss of the season, allowing five runs in six-plus innings as the New York Mets beat the Arizona Diamondbacks 9-1.
Jonathan Papelbon locked down his 16th save of the season as the Philadelphia Phillies beat Pittsburgh 3-1 to snap the Pirates' winning streak at nine.
Derek Norris cracked a go-ahead three-run homer in the eighth to lift the Oakland Athletics to an 8-7 win over the Chicago Cubs.
Torii Hunter singled in the tie-breaking run in the eighth as the Detroit Tigers edged out the Toronto Blue Jays 7-6.
Robinson Cano hit his 20th long ball of the season in the New York Yankees' 7-3 win over the Minnesota Twins.
Justin Upton scored three times on three hits to help the Atlanta Braves beat the Miami Marlins 11-3, while the Los Angeles Angels were 5-1 winners over the St Louis Cardinals.
The Milwaukee Brewers beat the Washington Nationals 4-0, the Chicago White Sox were 5-2 winners over the Baltimore Orioles and the Cleveland Indians held off the Kansas City Royals for a 6-5 victory.