Di Francesco's men climbed out of the drop zone courtesy of their nail-biting 4-3 win at high-flying Fiorentina on Tuesday, with striking sensation Domenico Berardi netting a first-half hat-trick.
The result, Sassuolo's third win in five games, saw the club (31 points, -30) move two points clear of the relegation zone, ahead of Chievo (30 points, -22), Bologna (29 points, -28), Catania (26 points, -34) and Livorno (25 points, -35), with two games remaining.
And Di Francesco, who was sacked in January only to be reinstated in March, says Sassuolo are up for the fight.
"Against a very strong side we fought with quality and hard work, deservedly getting the victory for what we showed in the opening 70 minutes," Di Francesco told Sky Sport Italia post-game.
"There is no such thing as an easy game and Fiorentina really played today, giving us a battle.
"The result of Catania-Bologna this weekend will be fundamental in the race for safety, as it's even possible 35 points could be enough."
The 44-year-old tactician also paid tribute to Berardi, who was the hero again for Sassuolo.
Berardi, on loan from Italian champions Juventus, has now scored three hat-tricks this season, having netted a treble against Sampdoria and four against AC Milan.
"He is young and at times makes some naive mistakes," Di Francesco said. "He has a strong character and without that he wouldn't play the way he does in big games.
"Curiously, whenever Berardi scored a hat-trick or even four goals, we ended up winning 4-3."
Meanwhile, Fiorentina boss Vincenzo Montella lauded goalscorer Giuseppe Rossi, who returned from injury.
The Italy international, sidelined since January with knee ligament damage, made his first league appearance in over three months, coming off the bench to spark a comeback for the home side.
"He is an extraordinary player, as when he's not in great shape he still manages to find that moment of magic from a champion," Montella said.
