Volavola’s opposite Tomasso Allan had kicked a penalty three minutes earlier to draw Italy level with Fiji at 19-19 after it had trailed throughout the match.
A draw seemed the likely outcome until lock Leone Nakarawa led a length-of-the-field breakout by Fiji with fulltime almost showing.
The 95-meter raid almost ended in a remarkable match-winning try to Jale Vatubua but the centre dropped the final pass with the goalline open.
Fiji stayed on attack, won a penalty advantage with time up on the clock and Volavola calmly drop kicked the ball between the posts to give the home side victory.
Fiji scored twice in the first half, through centres Eroni Vasiteri and Vatubua, to lead 14-9 at halftime. They extended their lead to 19-9 early in the second half with a third try to Vereniki Goneva.
Allan kept Italy in the match, kicking five goals from five attempts. He landed three penalties before halftime, then converted a 53rd minut try to lock Maxime Mbanda which came from a well-executed rolling maul.
Fiji paid heavily for a lack of discipline, conceding eight penalties at scrum where the Italian pack was overwhelmingly dominant. Tenth-ranked Fiji still managed to hang on and to eventually snatch a win which will boost its confidence ahead of next weekend’s clash with Scotland.
“It was a good performance by Italy,” Fiji captain Akapusi Qera said. “We were expecting that tough challenge from them.
“On our side, the boys hung in there. It was a tough workout for us and a good buildup to the game against Scotland.”
Italy play Australia at Brisbane this Saturday.