The former River Plate playmaker played from the start against Palermo and put Roma ahead in the seventh minute.
The home side squandered numerous chances to extend their lead but held on for three points.
The result lifted Roma to sixth in the standings, one point clear of Palermo, who are still winless on their travels this season.
Roma coach Luis Enrique, who was still without injured captain Francesco Totti, had demanded an immediate reaction from his side after last weekend's 2-1 defeat at Lazio in the city derby.
Palermo made the stronger start and had the first chance after four minutes when Eran Zahavi's low right-footed shot was kept out by Roma goalkeeper Maarten Stekelenburg.
The home side went ahead soon after.
Daniele De Rossi fed Lamela inside the area and he struck the ball towards the bottom left corner where Palermo goalkeeper Alexandros Tzorvas could not reach.
Roma could have doubled their lead in the 15th minute but Daniel Osvaldo's header from Marco Cassetti's cross went wide.
Palermo looked to hit back and had two great chances to do so before the break.
Giulio Migliaccio nodded over the bar in the 35th minute, while shortly afterwards Abel Hernandez's goalbound strike from the edge of the area forced Stekelenburg to fully stretch to clear his shot.
Roma had the first opportunity of the second half as Daniel Osvaldo got his head behind De Rossi's cross but his close-range effort went high.
The home side continued to press forward and Lamela almost added a second but his left-footed strike from 10 yards went wide.
Palermo showed more determination after the hour mark and Zahavi turned and sent his shot wide of the far post from 19 yards.
In the 70th minute, Mauricio Pinilla's close-range header went over the bar as another chance went begging for the visitors.
Substitute Fabrizio Miccoli could have snatched a point in the dying seconds but his 20-yard strike was kept out by Stekelenburg.