Tuesday's game was the first time the clubs have played in Cleveland since the epic 2016 World Series.
Chatwood (1-3) struck out five and walked five. He was lifted in favor of reliever Steve Cishek in the seventh after allowing a leadoff single to the Indians' Tyler Naquin.
Josh Tomlin (0-3) took the loss after surrendering five runs on seven hits in 3 2/3 innings. Four of the hits he allowed were home runs. Tomlin struck out three and didn't issue a walk.
Ian Happ had three of Chicago's 15 hits, and he added two RBIs and two runs. All nine batters who started the game for the Cubs had hits.
Cleveland managed nine hits off four Chicago pitchers, with Jose Ramirez and Bradley Zimmer collecting three each.
The Cubs (11-9) broke through against Tomlin in the second on Schwarber's solo home run and a single by Happ that drove home Addison Russell.
Willson Contreras ripped a solo homer over the left field fence in the third to push Chicago's lead to 3-0. Cleveland got on the scoreboard in the bottom of the frame when Jason Kipnis' groundout plated Zimmer.
Schwarber's second home run led off the fourth, and two outs later, Happ ripped a solo shot that staked the Cubs to a 5-1 lead and chased Tomlin.
Chicago expanded the lead to 8-1 in the seventh on a bunt RBI single by Albert Almora Jr. that sent home Jason Heyward, a groundout by Javier Baez that scored Happ, and a single by Tommy La Stella that plated Almora.
Edwin Encarnacion's infield single in the eighth and Erik Gonzales' single in the ninth accounted for the Indians' other runs.
Chicago added its final runs in the ninth on an RBI single by Anthony Rizzo and groundout by La Stella.
The series concludes Wednesday, when Chicago left-hander Jon Lester (2-0, 3.10 ERA) will oppose the Indians right-hander Trevor Bauer (1-2, 2.67).
--Field Level Media
Chi. Cubs | Cleveland | |
Tyler Chatwood | Player | Josh Tomlin |
Win | W/L | Loss |
6.0 | IP | 3.2 |
5 | Strikeouts | 3 |
4 | Hits | 7 |
1.50 | ERA | 12.27 |
Chi. Cubs | Cleveland | |
Ian Happ | Player | Jose Ramirez |
3 | Hits | 3 |
2 | RBI | 0 |
1 | HR | 0 |
6 | TB | 4 |
.750 | Avg | 1.000 |