Marek Hamsik and Gonzalo Higuain looked to have sealed victory for the hosts but Rodrigo Palacio halved the deficit before his fellow Argentine chipped home a late spot-kick
The Giallorossi's draw with Chievo earlier on Sunday paved the way for the Partenopei to move within two points of the automatic Champions League places in the clash at the San Paolo.
It appeared as though that would be the case, as Marek Hamsik's 51st-minute header and a superb long-range strike from Gonzalo Higuain put Napoli deservedly in control.
However, the visitors hit back via Rodrigo Palacio with 18 minutes remaining and the turnaround was completed in the 87th minute courtesy of Icardi's chipped penalty, after Henrique had received his second yellow card for a tug on Fredy Guarin.
Ultimately, Napoli coach Benitez - who had an unhappy spell as Inter boss between June and December 2010 - was left to rue a series of missed first-half chances, with the usually clinical Higuain particularly wasteful.
A draw changes little for either side in terms of their league standing, with Inter six points adrift of the Europa League places.
The home side started well and Higuain worked half a yard on the edge of the box before forcing a smart one-handed save from Samir Handanovic.
The lively Higuain was sent clear by Hamsik down the right in the 13th minute, but the angle proved too tight and he dragged his shot wide of the far post.
Higuain then saw a tame chip palmed away by Handanovic before the Argentina international missed the best chance of the match in the 31st minute.
Hamsik played in Dries Mertens down the left and his cross to the back post just needed Higuain to side-foot home the simple volley, but he somehow blazed wide.
The breakthrough finally came six minutes into the second half.
Jose Callejon picked out Henrique's overlap on the right flank and the full-back's pinpoint cross was headed home nonchalantly by Hamsik.
The goal seemed to force Inter into action as first Icardi glanced a header wide from Xherdan Shaqiri's cross, before the latter's whipped corner was headed over the crossbar by Danilo D'Ambrosio.
But the visitors' spell of dominance was brief as Higuain finally got his name on the scoresheet in the 63rd minute.
The striker collected Hamsik's short pass before curling an unstoppable 20-yard shot past Handanovic - the ball clipping the right-hand post on its way in.
Inter were handed a late lifeline, though, as Palacio drilled home from eight yards following a bout of pinball in the Napoli penalty area.
And Napoli's capitulation was complete with three minutes remaining, as Henrique was given his marching orders for a foul on Guarin and Icardi kept his cool from the spot to level it up.