The veteran striker pounced after seven minutes to power into the back of the net from close range after forcing his way into the Napoli box and rounding goalkeeper Mariano Andujar.
Emil Hallfredsson provided the assist for the second six minutes into the second period, pulling the ball into the centre of the penalty area from the left for Toni to guide home.
Verona had Jacopo Sala dismissed for a second bookable offence in the 90th minute, but it was too late for Napoli to make the most of the man advantage.
The result leaves Napoli fourth, having slipped behind Lazio in the race for the top three, while Verona pull 11 points clear of the relegation zone.
Cesena remain embroiled in the fight against the drop, but will attract huge credit for earning a 1-1 draw at Inter.
Inter looked likely to end disappointing run of three matches without a win in all competitions as they started the brighter, but fell behind to a Gregoire Defrel lob.
The home side upped their game after the break and, after Mateo Kovacic had seen an overhead kick ruled out for offside, Rodrigo Palacio restored parity from a Mauro Icardi cross.
For all their pressure, though, Inter were unable to find the winner – Lukas Podolski coming closest when he powered an effort against the post.
The result lifts Inter to seventh, while a point is not enough to haul Cesena out of the relegation zone.
Beleaguered Parma's miserable season continued as they were beaten 4-1 at Sassuolo having been reduced to 10 men on the hour, while Atalanta managed to hold on for a goalless draw against Udinese after having Carlos Carmona sent off late on.
In the day's other fixture, Chievo won 2-0 at Genoa, who slip below Inter to eighth.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.