Visitors Ajax had looked comfortable after former Southampton winger Tadic set up the first goal with a swerving cross before drilling home the second himself.
Red Star, who won the European Cup in 1991 and reached the latter stages the following season, finished second in Group H behind Arsenal who crushed BATE Borisov 6-0.
Ajax were joined by Young Boys, who stunned Dinamo Zagreb 2-1 away for a 3-2 aggregate win over the Croatians, and AEK Athens who scraped a 1-1 home draw with FC Vidi after a 2-1 win in the first leg in Hungary.
Former European champions Red Star Belgrade, Ajax Amsterdam and Celtic all made it comfortably through to the third qualifying round of the Champions League on Wednesday after surviving away legs.
Aseem Chhabra lists his favourite films, most of them shown at international film festivals held virtually (Berlinale and Rotterdam), hybrid (Toronto) or physical (Cannes and Venice).
Barcelona have vowed to use all legal means to fight a second fine imposed by UEFA after fans displayed pro-Catalan independence flags during September's Champions League Group E match at home to Bayer Leverkusen.
News of all that's transpired on and off the football field
Chelsea struck the woodwork twice but could not find a breakthrough in an entertaining 0-0 Champions League draw at Dynamo Kiev on Tuesday that left everything to play for in Group G.
Manchester United were given a troublesome tie against Club Bruges in the draw for the Champions League playoff round on Friday, although it could have been worse as they avoided Lazio, CSKA Moscow or Monaco.
Two late goals in two minutes from Sergi Roberto and Luis Suarez gave European champions Barcelona a dramatic 2-1 win over Bayer Leverkusen in the Champions League on Tuesday.
'The system is the same and we all have to contribute a bit more but it is impossible not to feel Messi's absence' 'But Neymar is also a leader for his playing style and what he brings to the team'
Troubled AC Milan were held to a goalless draw by AEK Athens
European champions Real Madrid will face former champions Liverpool, FC Basel and debutants Ludogorets of Bulgaria following the draw for the group stage of the Champions league on Thursday.
Lionel Messi is set for his first start for nearly two months when Barcelona, fresh from pulverising Real Madrid 4-0 at the weekend, set their sights on Champions League qualification when AS Roma visit the Nou Camp on Tuesday.
Barcelona strike duo Neymar and Luis Suarez have developed in the absence of Lionel Messi.
Lionel Messi's injury is a painful blow for Barcelona but is also a motivation for the rest of the squad, midfielder Ivan Rakitic said before the holders host Bayer Leverkusen in Champions League Group E on Tuesday.
News of all that's transpired on and off the football field
The goal machines of Bayern Munich, Chelsea and Shakhtar Donetsk cranked into top gear on Tuesday as the Champions League captivated its continental audience with a record 40 goals in one eight-game night.
Chelsea's Ruben Loftus-Cheek had a Europa League night to remember by scoring the first hat-trick of his career as the midfielder inspired them to a 3-1 home win over Belarus champions BATE Borisov on Thursday.
A summary of Thursday's matches in Europe's second tier club football tournament
Putin, who was received by External Affairs Minister Sushma Swaraj on his arrival, went straight to Modi's official Lok Kalyan Marg residence where the two leaders had a one-on-one meeting.
Summary of sports events and persons who made news on Friday
Arsenal will not sell striker Olivier Giroud, midfielder Jack Wilshere and winger Theo Walcott in the January transfer window despite their lack of playing time at the Premier League club, manager Arsene Wenger has said.
Arsenal and Chelsea were among seven teams to reach the Europa League knockout stage on Thursday, while last year's runners-up Olympique de Marseille were eliminated at the group phase.
It was the ninth consecutive victory for Dortmund in all competitions this season and showed they had put last season's disappointing performances behind them.
AS Roma supporters may be looking ahead to Barcelona's Champions League visit with some trepidation and coach Rudi Garcia certainly does not seem to be bursting with optimism.
Former Arsenal star Alexander Hleb says he made a mistake by leaving the Emirates to join Barcelona in 2008, and expressed regret at turning his back on managerial 'great' Arsene Wenger.
Cristiano Ronaldo took his tally for the La Liga season to a phenomenal 13 goals in six appearances with his third treble of the campaign as Real Madrid romped to a 5-0 win at home to Athletic Bilbao on Sunday.
News of all that's transpired on and off the football field
Ruthless Bayern Munich scored five goals in the first 35 minutes on the way to a 7-1 demolition of AS Roma on Tuesday which bore an uncanny resemblance to Germany's win over Brazil by the same score in the World Cup semi-final.
Manchester United ended their one-year Champions League hiatus in emphatic style when Wayne Rooney struck a hat-trick in a 4-0 destruction of Club Bruges that sent the three-times winners through 7-1 on aggregate on Wednesday.
On a night of close finishes in all five first-leg playoff games, the 21-year-old Dutch winger opened his United account with a memorable performance in the famous number seven shirt previously worn by George Best, Eric Cantona and David Beckham.
As Barca prepare for a trip to Madrid to play Rayo Vallecano on Saturday, they are still reeling from Tuesday's 3-2 Champions League reverse at Paris St Germain, when their defence was badly exposed by the Ligue 1 title holders.
Edinson Cavani scored early for Paris St Germain but a series of wasted chances came back to haunt them as Ajax Amsterdam equalised late to deny the French a winning start on the road in a 1-1 draw in Champions League Group F on Wednesday.
A Neymar double and a clinical finish from Luis Suarez handed Barcelona a comfortable 3-0 victory over BATE Borisov that put them on the verge of qualifying for the last 16 of the Champions League for the 12th consecutive season.
Real Madrid and Barcelona pulled two points clear in La Liga when Cristiano Ronaldo set a club scoring record in Real's 3-0 stroll against Levante and Neymar hit four as Barca beat Rayo Vallecano 5-2 on Saturday.
The Champions League group stages took on a less predictable look after Thursday's draw, helped by UEFA's decision to tweak the seeding system.
The three teams with 100 percent records in this season's Champions League can secure their places in the knockout stage this week with two games to spare.
Bayern Munich carved out a 1-0 win at CSKA Moscow on Tuesday thanks to Thomas Mueller's first-half penalty in the strangely muted atmosphere of a cold, damp and deserted Khimki Arena.
Photos from the Euro 2016 qualifying matches played on Sunday.