Spinazzola put Roma ahead with a 'Route One' goal in the 12th minute. Goalkeeper Antonio Mirante sent a long clearance upfield which flew over Fiorentina's back line and Spinazzola raced away, cut inside a defender and fired a low shot into the net.
Henrikh Mkhitaryan set up the second in the 70th minute with a low cross for Pedro which the Spaniard tapped into the net from close range.
Roma, who have 11 points from six games, are unbeaten on the pitch in all competitions this season although they were penalised with a 3-0 defeat by Verona -- a game that ended 0-0 -- for irregularly fielding Amadou Diawara.
Fiorentina, struggling for consistency, have seven points.