Cleveland responded Sunday, rewarding Francona with a 6-4 win over the Toronto Blue Jays.
David Murphy hit a three-run double in the sixth inning and John Axford worked out of bases-loaded jam in the ninth as the Indians avoided a series sweep and broke a three-game losing streak.
The Indians won 92 games and made the playoffs as wild-card team last season by getting contributions from as many areas as possible. That formula, which had been missing for much of the early season, was a key element against the Blue Jays.
"That's probably the best way we are as a team," Francona said. "That's the way we're built, get it across the board."
Francona didn't want his players dwelling on their 7-10 start going into Sunday.
"Nobody likes coming to the ballpark and look at your record when it's not what you want it to be," he said. "That's plain and simple. Saying that, I don't want them dragging in here, because it's a new day. During a baseball season there's a lot of grinding that needs to be done. Sometimes the game's easier than it is (at other times). That's simple fact. So when it's not going perfect, you grind the best you can."
"Hopefully, this is exactly what we need to get on a roll," Murphy said. "We haven't been playing terrible, but we haven't been playing characteristic of ourselves."
Cleveland entered the sixth trailing 4-2, but reliever Aaron Loup (1-1) walked the bases loaded before Murphy delivered a line drive past third base that kicked off the stands and caromed into shallow left field, allowing all three runners to score.
Axford, the fourth Cleveland reliever, loaded the bases with two outs in the ninth before retiring Edwin Encarnacion on a groundout.
Josh Outman (3-0) recorded the final out of the sixth and Cleveland's bullpen pitched 3 1-3 innings of scoreless relief.
Michael Brantley hit a solo homer in the second and added an RBI double in the fourth.
Toronto scored three times on four hits in the fourth. Jose Bautista and Juan Francisco had RBI singles while Brett Lawrire added a run-scoring groundout.
Brandon Morrow allowed three runs and was pulled after Nick Swisher's leadoff single in the sixth. Loup got Jason Kipnis on a fielder's choice. After Kipnis was caught stealing, Loup walked Carlos Santana, Brantley and Asdrubal Cabrera to fill the bases.
Murphy's liner past third bounced off the stands a few feet beyond the tarp and rolled into shallow left. By the time Melky Cabrera tracked it down, the runners had raced home and Cleveland had the lead.
"That's about as tough a lefty that I'm going to face," Murphy said. "Fortunately, he gave me a good pitch to hit."
"Walks hurt you," Toronto manager John Gibbons said. "These guys laid off it pretty good. And of course Murphy ends up getting the big hit there. We made a run at it late, it just didn't happen."
Carlos Carrasco retired the first nine hitters, but Jose Reyes led off the fourth with a double. Melky Cabrera's single sent Reyes to third before Bautista's single to right tied it. Francisco's single scored Cabrera and Lawrie's groundout made it 3-1.
Reyes added an RBI single in the fifth.
Carrasco hasn't recorded a victory in his last 16 starts. The right-hander's last win as a starter came on June 29, 2011, against Arizona. His last victory came in a relief appearance on Aug. 20, 2011, against the Los Angeles Angels.
Carrasco, who missed the 2012 season because of elbow surgery, is 0-11 with an 8.28 ERA since his last win as a starter.
NOTES: Bautista has reached safely in all 19 games. ... The Blue Jays are off Monday and begin a three-game series at home Tuesday against Baltimore. .... The Indians are expected to activate DH Jason Giambi (broken rib) from the 15-day DL Monday. He was hit by a pitch in a spring training game. ... Cleveland opens a four-game series against Kansas City at Progressive Field on Monday. RHP Zach McAllister (2-2) faces RHP Jeremy Guthrie (2-0).