Partizan had drawn level in the second-half but goals by substitute Theo Walcott and Samir Nasri ensured Arsene Wenger's side progressed second in the group behind Ukraine's 2009 UEFA Cup winners Shakhtar Donetsk - they beat Sporting Braga 2-0.
Elsewhere two of France's fallen stars Karim Benzema and Franck Ribery ensured they would get positive headlines for once.
Benzema - who was left out of the France World Cup finals squad after struggling to make an impact at Real Madrid - scored a hat-trick for Real Madrid in a 4-0 romp over Auxerre.
Ribery - who has had a wretched year on and off the pitch - scored his first goals for his club since April in Bayern Munich's 3-0 victory over Swiss side Basel, ruining the losers hopes of taking the second spot in the group from AS Roma.
Roma rounded off their campaign with a 1-1 draw away at Romanian side Cluj.
Bayern Munich showed there was no room for sentiment as they welcomed back former player Thorsten Fink and his Basel side, who entertained hopes of causing a shock and going through to the Last 16 at the expense of Roma.
However, Bayern struck twice in the first-half first through France playmaker Franck Ribery, with his first goal for the club since April.
Ukrainian Anatoly Timoschuk rattled home a second shortly afterwards leaving Fink - a Champions League winner with Bayern in 2001 and a loser in the dramatic final against Manchester United in 1999 - looking forlorn on the bench.
Fink was beside himself as early in the second-half Ribery hit his second of the match to wrap up the win and end the Swiss side's creditable campaign which at least sees them get the consolation of a place in the knockout stages of the Europa League.
There was also no victorious return for Ivory Coast football icon Didier Drogba to his former club Marseille, as the French champions beat the out of form English champions Chelsea 1-0 through a Brandao goal.
Chelsea were already assured of top spot in the table, with Marseille assured their place in the last 16 as group runners-up.
Real Madrid became the first side to score 300 goals (own goals included) in the Champions League main competition proper when Benzema netted early on.
The hosts doubled their advantage in the second-half with a peach of a goal by Cristiano Ronaldo and Benzema, who has been fighting to convince Jose Mourinho he is worth keeping did his case no end of good with a second and then added a third near the end.
The defeat ended Auxerre's hopes of grabbing third spot, but just for good measure Ajax pulled off a great result given they lost coach Martin Jol on Monday as they beat AC Milan 2-0 at the San Siro.
The four-time European champions scored both their goals in the second-half through Demy de Zeeuw and then Toby Alderwereild.
Spartak Moscow fans hardly gave a good account of what foreign visitors can expect at the 2018 World Cup as their boorish behaviour saw the match at Slovakian tailenders Zilina halted in the first-half when they threw flares onto the pitch.
Spartak ended up winning the match 2-1.