Zdenek Zeman's side posed a threat early on, only to be denied by the woodwork on three occasions in the first half.
And Genoa took full advantage, securing a first victory in six outings courtesy of goals early in the second period from M'Baye Niang and Iago Falque.
Luca Rossettini, Luca Ceppitelli and Paul M'Poku were the men who hit the frame of the goal for Cagliari, while Genoa also saw a number of opportunities go begging prior to the interval.
The restart was delayed due to an injury to referee Carmine Russo, who operated as a goalline official for the remainder of proceedings.
Genoa then made a chance count seven minutes after the break, Niang converting Facundo Roncaglia's cross from close range amid suspicions of offside.
Falque doubled the lead within six minutes, the forward sending a first-time finish back across goal after being played through by Diego Perotti.
The woodwork was struck again late on when Niang hit Zeljko Brkic's left-hand post with a thunderous effort from the edge of the area, but there were to be no further goals.
Cagliari remain 19th in the table, five points from safety, while Genoa are seven points shy of the top five.
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