Gonzalo Bergessio had grabbed a first-half lead for Catania, who looked dangerous through Spanish winger Keko, but Sassuolo hit back with three goals after the interval to leapfrog their opponents and leave the Sicilians bottom of the table.
Half-time substitute Simone Zaza levelled the scores before Simone Missiroli and Nicola Sansone made sure of Sassuolo's first win in nine outings, which moves them within three points of safety.
Ibrahima Mbaye was dismissed for a second yellow card with 10 minutes of normal time to play, and Innocent Emeghara's red card five minutes later put the hosts down to nine and gave Bologna a penalty, which Lazaros Christodoulopoulos converted.
Gianluigi Buffon had earlier saved an Emanuele Calaio penalty, while Pablo Daniel Osvaldo saw two efforts chalked off for offside as Juve struggled in the absence of the league's top scorer, Carlos Tevez.
Milan's week of misery continued as fan protests preceded a 4-2 home loss to Parma, who recorded a first Serie A win at San Siro since 1996.
Parity lasted less than two minutes though, substitute Amauri flicking in as Parma's bid for a European place gathered pace with their 16th league game without defeat and fifth Serie A away win in a row, sealed by Jonathan Biabiany's late header.
Two clubs troubled by off-field unrest, Cagliari and Lazio, met at Stadio Sant'Elia, with the capital club triumphing 2-0.
Lazio boss Edy Reja has overseen a recent upturn in form, and goals in each half from Senad Lulic and Balde Keita saw them rise to seventh place with a third win in four league games.
