Marquinho had put Roma ahead near the end of a first half the hosts had dominated, during which Fernando Gago missed a sitter at 0-0.
Napoli fought back in the second half, equalising through a wonder-goal from Juan Camilo Zuniga, and going in front thanks to a similarly spectacular strike from the otherwise quiet Edinson Cavani.
With the crowd on their backs and time running out Roma snatched a late equaliser when trickery from Ivorian forward Junior Tallo allowed fellow substitute Simplicio to volley home from close range, the Brazilian midfielder celebrating wildly as he climbed into the stands to kiss his family.
The result keeps Roma in seventh place, four points behind the Champions League places with three matches remaining, while Napoli go third, above Lazio on goal difference, although the Biancocelesti play on Sunday.
It was very much a game of two halves as Roma responded to fan protests with a ferocious opening 45 minutes that saw Francesco Totti go close with a pair of free-kicks, Fabio Borini put wide twice and Napoli keeper Morgan De Sanctis save from Rodrigo Taddei and Marquinho.
Then came Gago’s Ronni Rosenthal moment, the Argentine midfielder somehow placing his finish wide from close range after De Sanctis could only parry Totti’s deflected shot into his path.
It was a horrible miss that was followed up by Marquinho putting a free header over the bar after another fine delivery by Bojan, livelier than ever on the flanks.
Roma finally got the goal that their play deserved when Marquinho thrashed a finish into the roof of the net after a wicked low cross by Aleandro Rossi, who was released by a lovely Totti through-ball.
It seemed they would overrun Napoli, but clever tactics by visiting coach Walter Mazzari changed the face of the game.
Roma had been lightened in midfield due to suspensions for Daniele De Rossi and Erik Lamela, and the decision to ask Marek Hamsik to sit deeper saw the visitors overrun Roma early in the first half.
Their equaliser was a touch of class too: as Roma continued to contest what they felt was a contentious corner, it was taken short for Zuniga to work some space and fire a thunderbolt into the top right corner from the left side of the area.
The match had opened up, with Roma throwing caution to the wind as they desperately chased a win to appease fans who had booed every play bat Totti prior to kick off: Marquinho hammered a low shot just wide, their best chance as they piled men forward.
But, with Blerim Dzemaili replaced by the more direct Goran Pandev, Napoli were finding acres of space on the counter attack as Cavani, Gokhan Inler, Zuniga again and Christian Maggio all had decent chances finish off target or close enough for Bogdan Labont to save.
That was until Cavani struck on 67 minutes, the Uruguay star more impressive defending set pieces than going forward before he showed a flash of the genius that made him Europe’s most sought-after striker.
Pandev created the chance, the Macedonia forward excellent after his introduction and picking out Cavani with a fine through ball: the former Palermo striker still had it all to do but bought a yard off the sluggish Simon Kjaer before spanking a vicious shot across Labont and inside the top right, an almost carbon-copy finish to Zuniga’s.
Roma were in a panic, although they were struggling to carve out chances with Miralem Pjanic and Borini particularly disappointing.
Pjanic was soon withdrawn, Simplicio on in his place, but Borini survived as under-fire coach Luis Enrique made the strange decision to withdraw the sparky Bojan.
His replacement Tallo had the desired effect though as, having impressed with a show of power and guile in his cameo, the Ivorian weaved inside and out of Maggio on the left before curling a beautiful cross that left Federico Fernandez and Salvatore Aronica floundering to allow Simplicio a poacher’s finish at the far post.
With one minute of normal time remaining, the equaliser sparked a frantic finish, but neither side was able to win it, Gabriel Heinze making a game-saving block in the dying seconds after Hamsik almost sent Maggio clean through.
Despite the good performance and positive result, Roma fans still booed at the final whistle, apparently more concerned with the short-term gain of a couple of places and points than the long-term project set out by young coach Luis Enrique.
Napoli, meanwhile, continue to see their Champions League dream slip away as they pay for the poor run that followed their Champions League exit to Chelsea.