The ex-Giallorossi striker scored deep into second-half stoppage time to settle a heated encounter between Serie A's top two sides and put Juve on the brink of history
Goalkeepers Marco Stotari and Lukasz Skorupski were the stars of the show in a heated encounter between the sides, with neither team looking likely to break the deadlock after a fiercely-competitive 90 minutes.
However, Italy international Osvaldo - who was greeted by a chorus of boos from the home crowd as he came on in the second half - converted Stephan Lichsteiner's cross to seal all three points for the newly-crowned champions.
Juve move on to 99 points, beating the tally set by Inter in 2006-07, as Antonio Conte's men stand on the edge of reaching triple figures.
The kick-off time at Stadio Olimpico was brought forward by three hours following trouble in the capital before last week's Coppa Italia final.
It did little to dampen the atmosphere inside Roma's home ground as the supporters got behind their team, who started on the front foot but saw Francesco Totti and Mattia Destro fire off target.
Any fears that the game would be treated as a dead rubber were dispelled inside the opening half, which was played at a frenetic pace.
The visitors spurned an excellent chance to take the lead with 15 minutes gone when Carlos Tevez worked room for a shot inside the box but scuffed tamely wide.
Just a minute later at the other end, Vasilis Torosidis was denied his second league goal of the season after being adjudged to have handled the ball over the line.
Top scorer Destro wasted an opening when a heavy touch allowed Storari to save, while Roma debutant Skorupski made two good stops from Fernando Llorente as the contest became increasingly open.
Indeed, Juve's defence was wide open six minutes before the break when Gervinho raced through on goal, but he was thwarted by the onrushing Storari.
The woodwork came to Roma's rescue on the stroke of half-time, Pogba's powerful drive striking Skorupski's left upright.
Chiellini was fortunate to avoid sanction when he appeared to elbow Pjanic in a defensive wall for Andrea Pirlo's ultimately wasted free kick around the hour mark.
Pjanic, who signed a new four-year deal before the game, took matters into his own hands and was booked for a blatant foul on Chiellini a minute later.
Skorupski was forced into an athletic save from Lichtsteiner and Storari produced a fine double stop to deny Radja Nainggolan and substitute Alessandro Florenzi.
But, as the clock ticked down, Lichtsteiner's cut-back was turned into the corner by Osvaldo - Roma's top scorer last season - to spark jubilant celebrations among the travelling support and move Juve to the brink of history while ending the Giallorossi 's unbeaten run at home in Serie A.