Ferrari's Carlos Sainz Junior. and Charles Leclerc, who had looked like topping the timesheets until the final minutes, were third and fourth. Leclerc was fastest in both Friday sessions at Imola.
Red Bull's triple Formula One world champion and overall leader Max Verstappen remained off the pace in sixth and behind Mercedes' George Russell, whose teammate Lewis Hamilton was only 17th.
Verstappen, back on track after a difficult Friday, did not complete a soft tyre run however.
Australian Piastri lapped with a best time of one minute 15.529 seconds on a clear and sunny day at Ferrari's home circuit.
Norris, winner of the previous race in Miami, was 0.300 slower.
Alonso brought out the red flags with 35 minutes remaining of the hour-long session after he lost control at the final Rivazza corner.
The Spaniard climbed out and returned to the paddock after being cleared at the medical centre.
Perez briefly brought out more red flags with five minutes to go when the Mexican went nose-first into the barriers at the Variante Alta chicane.
The action resumed with two minutes left and drivers jostling to get a final flying lap in.
Haas' Kevin Magnussen took to the grass runoff to avoid contact with RB's Daniel Ricciardo who was on the racing line, while Leclerc also passed Sainz aggressively in a bid to beat the clock.
