© AP Photos
The visitors had not lost on the road in Serie A this season, having won once and drawn five times, but were immediately under the cosh at the Stadio Olimpico.
Both Pjanic and Erik Lamela provided Osvaldo with early opportunities to open the scoring but the Italian twice shot wide from good positions.
Pjanic also had an attempt on goal during the opening period but his 25-yard strike was kept out by a diving stop from Jean-Francois Gillet.
Long-serving captain Francesco Totti and Osvaldo came close in the early stages of the second half before the hosts were awarded a controversial penalty.
Osvaldo stepped up to convert from 12 yards, and when Torino launched a late rally, Pjanic's deflected shot put the game to rest with three minutes remaining.