The striker latched on to a clever through ball from Erik Lamela and coolly slotted home from 10 meters.
The visitors squandered several chances to increase their lead and ended up hanging on to claim the points with a resilient defensive display.
Roma move up to 41 points, one ahead of Inter Milan who briefly went above them in the table with a 2-0 win at Chievo Verona on Friday.
After taking the lead, Roma continued to turn the screw and pegged Palermo back as they dominated possession in an open first half.
Lamela spurned the best opportunity to double their lead when he blasted straight at Palermo keeper Emiliano Viviano after turning his marker inside out in the penalty area.
Borini could have put the match to bed midway through the second half but shot narrowly wide after slaloming into the Palermo penalty area.
The hosts found their feet as the second half wore on although they could not find a way past Roma keeper Bogdan Lobont who pulled off an acrobatic save to deny Ezequiel Munoz with five minutes remaining.
