The Giallorossi got the win they needed to give themselves hope in the race for Champions League qualification, but results elsewhere ultimately meant the side finished sixth in Serie A.
Roma will play in the Europa League next term.
Lorenzo Pellegrini broke the first-half deadlock with a fine first-time volley inside the box - but Gervinho slotted over five minutes from time to give the visitors an unlikely equaliser.
But Diego Perotti ensured it would be a winning farewell for his captain, as he arrived late at the far post to win it in the dying minutes.
De Rossi was substituted off moments before the equaliser, receiving a prolonged ovation from a sold-out Olimpico crowd.
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It was a poignant night for the Giallorossi, with De Rossi and boss Claudio Ranieri both the subject of appreciative banners and chants from the fans.
And, perhaps affected by that atmosphere, the game itself rarely sparked into life - with Antonio Mirante making a couple of saves but otherwise untroubled prior to Gervinho's strike.
It looked like Roma had won it with Pellegrini's strike, an emphatic volley inside the box, but in the end they required a timely late strike from Perotti to decide things.
The win secured, attention turned to sending De Rossi off in fitting fashion.
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