Novara started well and were much the better side in the first half-hour, but the hosts gradually imposed themselves on the game and took the lead shortly before half-time.
Miccoli then drove them forward throughout the second half and set up Budan for the second time to make the game safe in the 72nd minute.
Palermo were forced back as Novara came out of the blocks quickly, Marco Rigoni forcing a comfortable save from Emiliano Viviano before Andrea Caracciolo shot over.
Another flurry of attacks from the visitors from the 20-minute mark also came to naught, Rigoni curling a free-kick wide before Leandro Rinaudo was off target from close range and Caracciolo's effort did not seriously test Viviano.
Palermo slowly came into the game as an attacking force, though Josip Ilicic shot wide and Andrea Mantovani got right underneath a headed attempt.
They went ahead in the 41st minute, though, when Miccoli crossed for Budan to head down and past keeper Samir Ujkani.
Miccoli was at the centre of all Palermo's best attacks in the second half, though he was flagged offside before firing against the post early on.
Budan fired Miccoli's cross wide before the latter was sent through one-on-one with Ujkani. He shot against the upright, though, and the keeper had time to get back into position and save Ilicic's follow-up.
When the second goal arrived it was in similar fashion to the opener, Miccoli crossing for Budan to head into the bottom corner from just outside the six-yard box.
Rigoni shot over from the edge of the penalty area as Novara looked to set up an exciting finish, but Palermo held out comfortably enough.