Aceves (3-1), recalled before the game from Triple-A Pawtucket, allowed one run, four hits and four walks in his third stint with the Red Sox this season.
Nava put the Red Sox up 2-0 on a third-inning, two-run homer off Chris Archer (1-2), who gave up two runs, four hits, four walks and struck out seven over four innings.
The Cleveland Indians recorded a series-clinching 5-2 win over the Texas Rangers with Jason Kipnis including a home run in his three hits.
The Indians had put together consecutive victories to clinch their first road series in a month, Mike Aviles homering as his side headed into a day off before a nine-game home run starting on Friday against Washington.
The Los Angeles Angels beat the Baltimore Orioles 9-5 with Erick Aybar hitting a bases-loaded triple and Albert Pujols homering during a six-run seventh inning to stop a four-game losing streak.
Hank Conger homered, Pujols had three hits and Howie Kendrick contributed two doubles to help the Angels avoid a three-game sweep.
Lorenzo Cain hit a tying, two-run homer off Jose Valverde with two outs in the ninth and Eric Hosmer had a winning single in the 10th as Kansas City overcame Justin Verlander's seven scoreless innings in a 3-2 victory over Detroit.
Oakland beat the New York Yankees 5-2 and Houston defeated Seattle 6-1.
Minnesota beat Philadelphia 4-3 in the inter-League game.
Starling Marte had a career-high four hits and scored four times as the Pittsburgh Pirates beat the San Francisco Giants 12-8 in the national League.
Neil Walker and Alex Presley homered for Pittsburgh and Jordy Mercer, Andrew McCutchen and Gaby Sanchez had three hits each as the Pirates set season highs for runs and hits.
The San Diego Padres had a three-game sweep over the East-leading Atlanta Braves, a 5-3 win seeing Edinson Volquez strike out a season-high nine in seven innings.
The Cincinnati Reds recorded a record 12th straight win at Wrigley Field, a 2-1 win over the Chicago Cubs coming courtesy of Mike Leake combining with Aroldis Chapman on a three-hitter and Todd Frazier hitting a tiebreaking home run in the seventh inning against Travis Wood.
The New York Mets defeated the St Louis Cardinals 5-1, Dillon Gee having his third straight stellar start, Lucas Duda hitting one of three Mets homers and New York scoring the most runs allowed by St. Louis rookie Shelby Miller in his young career.
The Milwaukee Brewers thumped the Miami Marlins 10-1 as Carlos Gomez had four hits, including two triples, and Jonathan Lucroy drove in four runs.
Washington beat Colorado 5-1 while the Arizona Diamondbacks scored four runs in the 12th inning to beat the Los Angeles Dodgers 8-6.