Alberto Gilardino set Genoa on their way in the 28th minute from the penalty spot before Alberto Bertolacci made it 2-0 before the interval.
Gilardino could have scored his second of the afternoon two minutes from time but saw another penalty superbly saved by Sassuolo goalkeeper Gianluca Pegolo.
The outcome was Genoa's first win since November 10 and lifted the Grifoni to ninth in Serie A.
Sassuolo, meanwhile, suffered their fourth straight defeat and are 18th in the table.
The hosts enjoyed a strong start and in the sixth minute Pegolo had to be alert to keep out a powerful header from Sebastian De Maio.
At the other end, Simone Missiroli nodded Domenico Berardi's cross wide.
Genoa had a golden chance to break the deadlock when the referee pointed to the penalty spot after Marcelo Gazzola held Luca Antonelli in the area.
Gilardino, who fought against the clock to recover from a shoulder injury in time for Monday's game, stepped up to take the penalty and struck a right-footed shot past Pegolo to put his side in front.
Missiroli was unlucky not to equalise in the 44th minute when his close-range header from Luca Antei's cross was kept out by Genoa goalkeeper Mattia Perin.
Genoa doubled their advantage one minute later when Moussa Konate's cross found Bertolacci in the box and he beat Pegolo with a right-footed shot.
The hosts continued to press forward after the break and in the 52nd minute Pegolo did well to clear Antonelli's stinging drive from 30 yards.
Sassuolo twice had the chance to reduce the deficit after the hour mark but substitute Simone Zaza's header from Domenico Berardi's cross went wide while Diego Farias' shot from 12 yards went off target.
In the 87th minute, Antonelli thought he had put his team 3-0 up only to see his goal-bound shot met by a fine save from Pegolo.
One minute later, Pegolo guessed correctly to save Gilardino's right-footed shot towards the centre of goal after the Genoa striker had been brought down by Paolo Bianco in the area.