Sassuolo were off to a flying start against the current Serie B strugglers when Lorenzo Pellegrini tapped home the rebound from Matteo Politano's strike after just four minutes at the Mapei Stadium.
But their hopes of hanging on for the win were upset in three second-half minutes, Ciano beating Sassuolo 'keeper Gianluca Pegolo from the spot nine minutes from the end after Luca Antei was adjudged to have tripped Andrea Cocco.
Sassuolo failed to respond, and the 'Neroverdi' were stunned soon after when Antonio Balzano powered down the right for Laribi, who is on loan from Sassuolo, to sweep a dramatic winner past Pegolo.
Cesena will now meet either Roma, or Sampdoria, in the quarter-final after their tie at the Stadio Olimpico on Thursday.
Later Wednesday Lazio host Genoa, while on Tuesday Antonio Candreva fired Inter Milan into the quarters with a 98th minute, extra-time winner against Bologna (3-2).
Napoli will face Fiorentina in the quarter-finals, when Juventus host AC Milan, who have beaten the Cup holders twice already this season, in the league and in the Italian Super Cup final.