Simone Pepe was the other scorer for Serie A leaders Juventus who stayed unbeaten this season after 15 games and went two points clear of titleholders AC Milan and Udinese.
Giampiero Pinzi finished off a slick counter-attack in the 74th minute to give Udinese, who began the season hoping to avoid relegation, a draw in an entertaining match.
Antonio Floro Flores had opened the scoring for Udinese in the 28th minute before Lazio replied either side of half-time through Senad Lulic and an own goal from Damiano Ferronetti who deflected Miroslav Klose's shot into the net.
AS Roma put recent internal problems behind them and won 3-1 at Champions League contenders Napoli, who are struggling to compete on two fronts.
An early own goal by Napoli goalkeeper Morgan De Sanctis put Roma on course and Pablo Osvaldo added the second just before the hour. Marek Hamsik pulled one back before Fabio Simplicio completed the scoring.
Andrea Ranocchia's second-half goal gave Claudio Ranieri's Inter their fifth win in six league games, 1-0 at Cesena, although they were somewhat lucky as the Sea Horses had most of the play and chances.
Parma scored twice in the last five minutes to draw 3-3 with Lecce, Genoa beat Bologna 2-1 and Catania overcame Palermo 2-0 in Sunday afternoon's other games.
Juventus are on 33 points, two ahead of AC Milan, who briefly went top with a 2-0 home win over Siena on Saturday, and Udinese. Lazio have 29 and Inter 23.
Quagliarella, who has a knack of scoring spectacular goals, last hit the net against Chievo on Dec 19 last year but shortly afterwards suffered a knee ligament injury which ruled him out for the rest of last season.
"This is the cherry on the cake," the Italy international told Juve's website. "It hasn't been easy in the last months but I've always felt I had the backing of the coach and the team."
Alessandro Del Piero was given a rare start this season for Juventus who needed only four minutes to break the deadlock and Pepe turned in Paolo De Ceglie's low cross at the far post.
Dominating the game, Juve missed a hatful of chances before Quagliarella headed in from a corner with 15 minutes left.
