Led by Dunn's long ball, the White Sox jumped into a 5-0 after two innings to hand Boston starter Jon Lester his first loss of the year, getting all their runs with two outs.
Jarrod Saltalamacchia hit a two-run homer in the third for Boston and Will Middlebrooks pulled them within two with a two-run double in the seventh, but it was not enough to stop their winning streak ending at five matches.
Vernon Wells and Travis Hafner each drove in a run in the 10th to give the New York Yankees a 6-4 win over the Baltimore Orioles.
Hafner had hit one of the Yankees' four solo homers in the ninth to take the game to extras, with the others coming from Robinson Cano, Lyle Overbay and, with his first in the majors, David Adams.
Chris Davis went yard for the Orioles.
Clayton Kershaw allowed just three hits as he pitched a complete game in the Los Angeles Dodgers' 3-1 win over the Milwaukee Brewers.
Kershaw struck out five and walked one in his second complete game of the season, while Andre Ethier homered and tripled.
Patrick Corbin fanned 10 in the first complete game of his career to lift the Arizona Diamondbacks to a 5-1 win over the Colorado Rockies.
Corbin scattered three hits and walked one for his seventh win of the season, while Didi Gregorius drove in a pair on three hits.
Yan Gomes' three-run homer in the 10th saw the Cleveland Indians to a 10-8 win over the Seattle Mariners - their third walk-off victory in a four-game sweep.
Ryan Raburn also connected for a three-run shot for the Indians, while Kyle Seager, pinch hitter Endy Chavez and, in the top of the 10th, Justin Smoak all went yard for the Mariners.
RA Dickey went a season-high eight innings, allowing three runs - two earned - for his second straight win as the Toronto Blue Jays beat the Tampa Bay Rays 7-5.
Julio Teheran allowed one run in 8 1/3 innings and Dan Uggla smashed a three-run homer in the Atlanta Braves' 5-1 victory over the Minnesota Twins.
Matt Dominguez belted a three-run shot in the Houston Astros' 6-5 win over the Kansas City Royals, Will Venable homered as the San Diego Padres' beat the St Louis Cardinals 4-2 and the San Francisco Giants routed the Washington Nationals 8-0.
The Oakland Athletics were 9-2 winners over the Texas Rangers, the Cincinnati Reds edged out the New York Mets 4-3 and the Miami Marlins overcame the Philadelphia Phillies 5-1.