The hosts started strongly and could have been ahead in the fifth minute but Emil Hallfredsson's effort was well saved.
Manolo Gabbiadini then got in behind for Sampdoria but his shot was tipped over the bar by Rafael in the home goal.
Fabrizio Cacciatore should have opened the scoring before the break but his header went wide when well placed.
Just five minutes into the second period Verona did take the lead through Juanito Gomez calm low finish.
The points were secured with just over 10 minutes left as Luca Toni drilled a low effort beyond the reach of the goalkeeper.