Juve, who have seven games remaining, can reopen their eight-point gap with victory over Livorno on Monday night, but nerves will be frayed in Turin after Roma demonstrated their determination to snatch the Scudetto.
Destro scored once in the first half and twice after the break to reach 13 goals for the season before Mauricio Pinilla gave 15th-placed Cagliari some reason to be cheerful by blotting Roma's clean sheet with a penalty at the death.
In the late game, Marco Parolo fired Parma into sixth place while seriously wounding Napoli's bid to finish second.
A strike of real quality 10 minutes into the second half proved enough to return Europa League-chasing Parma to winning ways following three defeats on the spin.
While their title bid has been over for some time, Napoli retain ambitions of catching Roma but now trail the capital club by 12 points.
Fourth-placed Fiorentina pulled five points clear of Inter Milan by edging a 2-1 home victory over Udinese.
Juan Cuadrado opened the scoring at the Stadio Artemio Franchi before Gonzalo Rodriguez's second-half penalty set La Viola on a course to win their first game in three attempts.
Bruno Fernandes ensured a nervous finale by surprising goalkeeper Neto with a cross-shot.
Ten-man Lazio maintained their push for a European place with a 2-0 victory over a disappointing Sampdoria.
Antonio Candreva scored his ninth goal of the campaign to put the Biancoceleste ahead in the 42nd minute.
Despite playing in numerical inferiority following the sending off of midfielder Lucas Biglia for a second yellow card early in the second half, Lazio doubled their lead through Senad Lulic in the 73rd minute.
Catania boss Rolando Maran was sacked after Torino scored twice in the final 11 minutes to clinch a 2-1 come-from-behind victory in Sicily.
Gonzalo Bergessio put the relegation-threatened hosts ahead after only two minutes at the Stadio Angelo Massimino, but substitute Alexander Farnerud drew Torino level in the 79th minute before Ciro Immobile netted a late winner.
The result lifts the Granata to 10th place in the table while academy coach Maurizio Pellegrino has taken control of the Catania first team ahead of a daunting season run-in.
Elsewhere, Nicola Sansone struck twice as second-bottom Sassuolo ended Atalanta's six-game winning run with a 2-0 triumph.
Sansone put the visitors in front in the 33rd minute and doubled their advantage after the interval as the Neroverde won for the second time away from home this season.
The outcome lifted Sassuolo to within three points of safety, while Atalanta dropped to eighth in the table.