Mattia Destro struck a second-half equaliser for Rudi Garcia's understrength side, leaving Juventus the chance to extend their lead to five points on Sunday
The hosts came into the tie unbeaten in their last six games and continued their habit of making good starts when they took an early lead through Paulo Dybala after just two minutes. The Sicilians have now scored 21 first-half goals this season, more than any other club in Serie A.
Davide Astori's stray pass was intercepted by Franco Vazquez, who rolled in his fellow Argentine to slot home the opener from close range.
It was Dybala's 10th goal of the campaign and the third time this season that Rudi Garcia's men had gone behind inside the opening three minutes.
A depleted Roma side were clearly missing the presence of Daniele De Rossi, Radja Nainggolan and Seydou Keita in a midfield that was persistently bypassed by a Palermo side who played with a real zip in the first half, frequently looking to get Vazquez and Dybala running at an often exposed visiting backline.
In a quiet first period the hosts could have doubled their lead five minutes before the break, but Morgan De Sanctis made a diving save to stop Edgar Barreto's header from 12 yards as Roma failed to secure a single shot on target in the opening 45 minutes.
The Giallorossi made a much more positive start to the second half, carving out their best chance of the match within a minute of the restart, but Mattia Destro could only head Jose Holebas' whipped cross over the bar.
The visitors continued to improve in the opening stages of the second period and managed to work Stefano Sorrentino for the first time on 52 minutes, though Miralem Pjanic's fierce strike was straight at the Palermo goalkeeper.
Roma continued to press and were level two minutes later when Pjanic's in-swining free kick from the left was nodded down by Kevin Strootman for Destro to stab home from inside the six-yard box.
Former Boca starlet Leandro Paredes was making his first start of the season and the Argentine made his first serious contribution on the hour mark when he tested Sorrentino from long range.
But for all Roma's improvement, Palermo should have been ahead a minute later as Baretto played in Dybala, but this time the Argentine's shot was blocked by a sprawling De Sanctis.
The draw means table-topping Juventus have the chance to extend their lead at the summit of Serie A to five points when they host Verona on Sunday.