The capital club took sixth spot from Inter Milan with a narrow win at the Stadio Renzo Barbera. Fabio Borini's goal in the third minute was enough to earn the Giallorossi all three points and inflict the second home defeat in a row on Palermo.
The hosts had fought back late on but could not find a leveller as Roma held on.
"I'm pleased with the win," Luis Enrique told his club's website. "All of my players did well out there and I want to congratulate every one of them.
"It's tough here in Palermo - one of the most difficult grounds to come to in Serie A - so we knew we would have our work cut out if we wanted to win. But I think we deserved the three points at the final whistle.
"We were good in the first half, then after the break Palermo brought on two tricky customers in (Josip) Ilicic and (Abel) Hernandez and they caused us a few more problems.
"All the same, apart from the last 10 minutes, I don't think we struggled particularly."
Palermo boss Bortolo Mutti will be fearing a call from club president Maurizio Zamparini after his side lost once again in front of their own fans after going down to AC Milan last week.