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, whose coach Bortolo Mutti will be fearing a call from club president Maurizio Zamparini.
Palermo responded well in the second half after suffering in the first, but they were unable to find a reply to Borini's early effort as they lost once again in front of their own fans after going down to AC Milan last week.
Roma did not luck too down after their derby defeat last weekend as they raced into the lead in the third minute.
Lamela pounced on a poor clearance by Ezequiel Munoz and then threaded the ball through the Palermo defender's legs into the path of Borini, who picked his spot low in the bottom left-hand corner of Emiliano Viviano's goal.
Lamela looked particularly motivated and he almost scored a second as he held off Munoz but saw his angled shot saved.
Palermo's biggest threat in the first half came from a succession of unintentionally mishit crosses which Bogdan Lobont had to push over his own crossbar.
Things had to change for the home side in the second half and Mutti sent Josip Ilicic and Abel Hernandez on.
Ilicic's 57th minute shot was saved at the second attempt by Lobont as Mutti's substitutions had the desired impact.
Apart from a Borini shot into the side-netting, the second half belonged to the home side, who went close to equalising when Lobont pushed a cross out to Miccoli, who shot straight back at the Roma goalkeeper with the goal gaping.
Munoz almost made up for his error on the Roma goal with a shot which required a good save from Lobont in the 85th minute as Palermo continued to attack in numbers.
The Palermo defender came close again in a goalmouth scramble in stoppage time which Roma somehow managed to clear with some desperate defending.
And they somehow managed to hold on for all three points to move back above Inter, five points adrift of fourth-placed Udinese.