The 33-year-old, who moved from Chelsea in July, picked up a loose defensive clearance well outside the penalty area before unleashing a thunderous strike that went in off the upright after 55 minutes.
Roma had collected only one point from their opening two matches but were catapulted into the top half of the standings after Saturday's success.
It was a third loss for Udinese, still seeking their first points of the new campaign.
But there were plenty of chances for the home team at the Friuli Stadium as they forced several key saves out of veteran Roma goalkeeper Antonio Mirante.
Kevin Lasagna, in particular, had a host of chances but failed to convert for Udinese.
Rainy conditions did not hinder a free-flowing game with Roma also squandering opportunities to win by a bigger margin.