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Alberto Gilardino threatened for the home side after just five minutes, showing great control to find space, but his shot was well blocked by the defence.
Genoa dominated possession in the opening 15 minutes, but struggled to create any clear chances as the Verona defence stood firm.
Matuzalem had an effort on goal from the edge of the area on 18 minutes, but his strike did not trouble the goalkeeper, who gathered well.
Genoa took the lead just before the half-hour mark through Daniele Portanova, who headed home from Matuzalem's corner to make it 1-0.
The home side doubled their lead on 34 minutes when Matuzalem's accurate lofted pass found Juraj Kucka, who steered his header past the goalkeeper from close range.
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Verona tried to push forward before the half-time whistle, but could not create anything in the last third.
Luca Toni came close to pulling a goal back for the away side two minutes into the second half, but he could only put his header from a free kick wide of the post.
Verona had a huge opportunity to get back into the game on 69 minutes through Bosko Jankovic, but he could not direct his headed effort on target.
Five minutes later, Jankovic had an effort from distance, although his strike went just wide of the mark.
Toni came close against on 80 minutes, hitting the post with a header before Daniele Cacia sent a weak shot straight at the goalkeeper from the rebound.