Central defender Mapou Yanga-Mbiwa was the unlikely hero as he headed the winner five minutes from the end of a feisty encounter that produced eight yellow cards, several skirmishes between players and numerous protests.
Third-placed Lazio, who needed a draw to make sure of a place in the Champions League playoff round, now have their hopes of qualifying in the balance while the chances of Napoli, who are fourth, have been rekindled.
The two sides meet in Naples on Sunday with the hosts needing a win to pip Lazio for third place and qualify at their expense.
Juan Iturbe put Roma ahead in the 73rd minute with his first goal since October before Filip Djordjevic headed Lazio level eight minutes later in a thrilling finale.
Earlier, Miroslav Klose had an excellent chance for Lazio after five minutes but the former Germany forward headed wide when he looked certain to score.
Tempers flared after Lazio midfielder Senad Lulic cynically felled Iturbe with a tackle from behind but, despite Roma players surrounding the referee demanding a red card, the Bosnian escaped with a booking.
Roma players were again demanding a red card for Lulic after he fouled Francesco Totti early in the second half. The referee was again unmoved and instead booked Vasilis Torosidis for dissent.
Lulic was substituted minutes later.
Miralem Pjanic injected new life into Roma when he came on in the 68th minute.
Victor Ibarbo, who replaced a lacklustre Totti, somehow fired wide from six metres when he was left unmarked but almost immediately made amends by producing a low cross that Iturbe turned in for Roma's opening goal.
Roma appeared to be on top until Felipe Anderson floated a cross to Klose at the far post and he nodded the ball on for Djordjevic to equalise.
Yanga-Mbiwa was at fault for that goal, allowing Djordjevic to get free, but made amends by heading in from Pjanic's free kick to ensure that Roma would finish second behind champions Juventus.
(Writing by Brian Homewood, editing by Tony Jimenez)
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