However, compatriots Lazio slumped to a shock 1-0 defeat at home to Ludogorets Razgrad in another first leg tie.
Osvaldo, signed on loan after a troubled and disappointing six months at Premier League Southampton, fired home with an angled shot in the 16th minute after the ball ricocheted to him.
Juventus, one of eight teams who parachuted into the Europa League knockout stage after finishing third in their Champions League groups, lived dangerously before Paul Pogba added the second from a Carlos Tevez pass in stoppage time.
Lazio's difficult season continued as they missed a penalty on their way to a defeat against the Bulgarian champions in a game which also featured two red cards.
Roman Bezjak sank Lazio with a swerving 25-yard shot on the stroke of half-time and Lazio's Felipe Anderson had a penalty saved after the re-start before Svetoslav Dyakov (Ludogorets) and Luis Cavanda (Lazio) were both sent off.
Elsewhere, Jonathan Soriano scored an incredible goal from near the halfway line to complete a stunning 3-0 win for Salzburg away to once-mighty Ajax.
Austrian Bundesliga leaders Salzburg, who won all six group stage matches, continued a remarkable season by outclassing four-times European champions Ajax in their own back yard.
Soriano gave Salzburg a 14th-minute lead with a penalty and Sadio Mane doubled the advantage with a clinical finish from Kevin Kampl's pass seven minutes later.
The highlight came in the 35th minute when Spaniard Soriano picked up a loose ball inside the centre circle, saw Jasper Cillessen off his line and scored with a looping effort which had the Ajax goalkeeper desperately chasing back in vain.
Dnipro Dnipropetrovsk coach Juande Ramos enjoyed a 1-0 win over his former club Tottenham Hotspur when Yevhen Konoplyanka converted an 81st-minute penalty following a foul by Jan Vertonghen on Matheus.
Valencia scored two late goals to beat Dynamo Kiev 2-0 in a match played in neutral Cyprus after being moved from Ukraine because of the clashes which have killed more than 70 people in Kiev since Tuesday.
New signing Eduardo Vargas headed in from a corner in the 79th minute and Sofiane Feghouli scored a fortuitous second with a wayward shot that hit Domagoj Vida and looped over the committed Kiev keeper Olexandr Rybka.
AZ Alkmaar also snatched a late win at Sloven Liberec following a mistake by goalkeeper Premysl Kovar, who spilled Nemanja Gudelj's free kick and allowed Nick Viergever to score into an empty goal in the 89th minute.
Porto squandered a two-goal lead in a 2-2 draw with Eintracht Frankfurt while Maribor and Sevilla also shared four goals.
Chernomorets Odessa were held 0-0 at home by Lyon, Anzhi Makhachkala's match at home to Genk also ended goalless as did the tie between Maccabi Tel Aviv and last season's semi-finalists Basel.