Only the Giants have won more, with 11,179 victories after starting in New York in 1883 and later moving to San Francisco.
The Cubs, who earned their first victory in 1876, improved to 11,000-10,414. The Brooklyn/Los Angeles Dodgers are close behind with 10,996 wins.
David Bote homered and drove in four runs for the NL Central-leading Cubs.
''We hit a lot of balls the other way tonight and you love to see that,'' Bote said. ''That means you are on it longer and you are seeing it a little deeper. That's what lets you drive it.''
Baez had three RBIs.
''This felt really, really good,'' said Baez, who came into the game hitting .122 in his past 12 games. ''I've been struggling, but I never stopped working. Today, I finally got the results and so did the team.''
Cubs starter Alec Mills (3-2) got the win, giving up three runs on seven hits and a walk while striking out seven.
''I wasn't throwing a lot of strikes early on,'' he said. ''After the third inning, I started throwing a lot more fastballs. It helps when the offense is scoring runs - I just didn't want to start walking guys and let them back into the game.''
Tigers top prospect Casey Mize (0-1) made his first home start, allowing four runs - three earned - on five hits and two walks in 3 1/3 innings. He struck out two.
''It was a pretty poor performance - I hate that I couldn't go more than 3 1/3 and put our team in a position to win,'' he said. ''I think the biggest learning point from this was that when I was throwing stressful pitches, I was gripping the ball and tensing up.''
''I've got to stay calm in those spots and just hit my spots,'' he said.
The Cubs took a 2-0 lead in the second inning on two-out, RBI singles by Bote and Nico Hoerner. Ian Happ walked to load the bases, but Anthony Rizzo popped out on the next pitch.
Jeimer Candelario had an RBI grounder for the Tigers in the third.
The Cubs scored four in the fourth, starting with Bote's leadoff homer over the Chicago bullpen in left-center field.
''The kid threw the ball really well tonight, which we expected after seeing his first start, but we were able to adjust to what he was doing,'' Bote said. ''That's the key, no matter who you are facing. You have to take away what they are doing well.''
Hoerner reached on an error, stole second and took third on a flyball. That ended Mize's night, and Rizzo greeted Tyler Alexander with an RBI single. Baez followed with a two-run homer to make it 6-1.
''He needed to attack more and get some early outs in order to get deeper into the game,'' Tigers manager Ron Gardenhire said. ''We're excited about him. It takes time, but he'll get there.''
Christin Stewart's two-run homer in the seventh cut the deficit to 6-3.
Baez hit a solo home run in the ninth and Bote added a two-run single.
The Cubs won their first game against Louisville on April 25, 1876. They reached 10,000 victories against the Houston Astros on April 23, 2008.
The teams play the second of three games Tuesday evening, with Spencer Turnbull (2-2, 3.65) starting against Tyler Chatwood (2-1, 5.40), who will be activated from the 10-day disabled list. Chatwood (back) last pitched on Aug. 6.
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