Baez capped a five-run first inning with a four-run blast to left-center off Reds starter Amir Garrett, who had just arrived from a brief minor league stint at Triple-A Louisville and was making his seventh Reds start of the season.
Cubs left-hander Jon Lester (2-2) worked five shutout innings before the Reds exploded for four sixth-inning runs. It was his first win since May 2 in a season featuring five no-decisions.
The Cubs (21-19) have won three straight while the Reds (19-21) have now lost six in a row.
Garrett (4-3) struggled right out of the gate en route to the loss. He loaded the bases in the first and walked in one run before giving up the grand slam to Baez as the Cubs opened a 5-0 lead.
The Baez homer, his sixth of the season, came on a 1-2 pitch and also plated Anthony Rizzo, Willson Contreras and Addison Russell.
The Reds left-hander settled down and allowed just two hits and walk over two scoreless innings.
But in the fourth he gave up a first-pitch solo home run to Kris Bryant that landed well beyond the center-field wall to make it 6-0. The estimated 450-foot shot was Bryant's team-leading eighth homer of the season.
Garrett departed for a pinch hitter in the fifth inning. He allowed six runs on five hits, walked four and struck out five in a four-inning outing, his first for the Reds since May 6.
Reds right-hander Blake Wood entered in relief and gave up three runs as a Baez had an RBI single, Lester hit a sacrifice fly and Ben Zobrist singled in another run.
Lester worked into the sixth inning when he gave up three straight singles, including an RBI base hit to Arismendy Alcantara that drove in Jose Peraza.
Reliever Hector Rondon took over when Lester departed with two runners on and none out. Rondon gave up a ground-rule RBI double to Billy Hamilton, and Zack Cozart's fielder's choice grounder brought home Alcantara.
Rondon then gave up a two-out single to Adam Duvall that scored Hamilton and cut the deficit to 9-4.
Lester, who entered the sixth with a shutout, was responsible for three of the runs. He also gave up six hits, walked one and struck out five.
Cubs reliever Brian Duensing loaded the bases in the ninth with none out, departing for right-hander Koji Uehara.
A Duvall sacrifice fly scored Hamilton, but Uehara struck out Eugenio Suarez and pinch hitter Stuart Turner to end the game and collect his first save.
Chicago collected nine hits while Reds pitchers walked nine more Cubs. Zobrist and Ian Happ each went 2-for-4. Suarez, Hamilton and Cozart each had two hits to lead the Reds.
NOTES: Cincinnati officially recalled LHP Amir Garrett from Triple-A Louisville prior to his Thursday start. ... The Reds return home to open a three-game weekend series against Colorado, sending RHP Lisalverto Bonilla (0-1, 4.85 ERA) against Rockies LHP Tyler Anderson (2-4, 6.43 ERA). ... The Cubs remain home for three games against the NL Central-leading Milwaukee Brewers. They'll have RHP Eddie Butler (1-0, 0.00) making his Wrigley Field debut on Friday against Brewers RHP Paolo Espino, making his major-league debut. ... Chicago OF Kyle Schwarber had Thursday off after starts in the leadoff spot in 34 of the Cubs' 39 games. He had reached base safely in his last nine games and had a .311 on-base percentage. ... In a pregame ceremony, Jackie Robinson's granddaughter, Meta, helped raise a flag up the Wrigley Field right field foul pole commemorating the 70th anniversary of Robinson's first game in Chicago on May 18, 1947, before a paid crowd of 46,572 fans, still the largest regular season house in Wrigley history.