The victory at the Juventus Stadium means that the Azzurri have finished top of Group B with 20 points from eight games, with two more rounds of matches still to come.
Balotelli was unlucky not to restore parity for the Azzurri five minutes later when his powerful shot from inside the area smashed against the crossbar.
Moments later the AC Milan striker was guilty of missing a sitter when he ballooned a loose ball over the bar from just yards out.
Cesare Prandelli's side pushed forward in search of an equaliser and could have got it six minutes from half time had Balotelli's header from point-blank range not been turned away by Cech.
Antonio Candreva tested Cech from 20 yards on the stroke of half time, before Kozak squandered a chance from a counter-attack for the Czechs.
Four minutes later the home side were awarded a penalty when Theodor Gebre Selassie brought down Balotelli inside the Czech penalty area.
The former Manchester City forward picked himself up and made no mistake in making it 2-1 to Italy from the spot.
The Czechs ended with 10 men on the pitch as Daniel Kolar was sent off for a second bookable offence in the 89th minute.