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Genoa took the lead after just three minutes when Sebastien De Maio finished neatly with his left into the top left corner of goal from the edge of the six-yard box.
The visitors pulled level just before half time when Marco Sau somehow found himself unmarked in the area, allowing him to slot the ball home into the centre of goal.
Sau almost gave Cagliari the lead after half time, but he saw his right-footed effort flash wide of the left post having been picked out by Ibarbo's pass.
Marco Motta wasted a good chance for Genoa with just over 20 minutes remaining as he jumped highest, but he could only send his header both high and wide of the target.
Genoa were to rue the miss as Ibarbo snatched all three points for Cagliari with eight minutes remaining when he drilled his shot into the bottom left corner.