The visitors made a fast start to the match and broke the deadlock with just two minutes on the clock.
Lazzari sent over a cross for Stevan Jovetic, who converted at the first time of asking.
The home side then began to control the fixture, but their efforts did not look as though they were going to be rewarded until 19 minutes from time. Argentine midfielder Fernando Gago threaded a pass through to Francesco Totti, who took one touch before sending the ball into the top corner of the net from 12 yards out.
Totti had a chance to steal all three points for Roma in the closing stages, but he shot wide of the target from 12 yards out.
His miss was punished in injury time when Lazzari scored from close range to give his side the victory.