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.
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.
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.
