Cagliari striker Leonardo Pavoletti showed great strength to control a long ball on his chest, turn his marker and power in a half-volley five minutes before halftime.
But the home side were awarded a penalty for handball following a Video Assistant Referee (VAR) review in the final minute of regulation time, which captain Criscito dispatched.
Genoa substitute Giuseppe Pezzella was then sent off deep into stoppage time for a rash challenge on Nicolo Barella.
Prandelli’s side are in 17th place on 37 points but Empoli are two points behind with a game in hand.
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Cagliari are now mathematically safe from relegation in 12th place on 41 points.
Genoa travel to Fiorentina for their final game of the league season next Sunday, while Empoli will be away to Inter Milan.
Earlier, Udinese’s survival hopes were boosted with a 3-2 win over SPAL, a victory that moved Igor Tudor’s side on to 40 points and ensures that they will remain in Serie A next season if Empoli fail to beat Torino.
(Reporting by Alasdair Mackenzie; editing by Clare Fallon)
