Sassuolo moved up to 11th, a point above Bologna, ahead of the rest of the weekend's fixtures.
Sassuolo had won just one of its six matches — home and away — since its last victory at the Mapei Stadium on Sept. 22.
Boga doubled Sassuolo's lead in the 68th, two minutes before Riccardo Orsolini reduced the deficit.
However, Caputo swiftly restored Sassuolo's two-goal advantage with a fine solo effort.
Orsolini, who received a debut call-up to the Italy squad earlier Friday, thought he had pulled another goal back for Bologna but it was disallowed for offside.