Chelsea opened the defense of its Champions League title by throwing away a commanding lead to draw 2-2 against Italian champion Juventus, while Barcelona needed two goals from superstar Lionel Messi to beat Spartak Moscow 3-2 after the Russian side had led 2-1.
Brazilian midfielder Oscar marked his first start for Chelsea with two long-range goals, but Arturo Vidal pulled a goal back close to halftime and substitute Fabio Quagliarella equalised late on.
Shakhtar Donetsk's comfortable 2-0 win against Danish debutant Nordsjaelland took the Ukrainian side top of Group E, with Armenian forward Henrik Mkhitaryan scoring in each half with excellent finishes.
In Group G, four-time champion Barcelona had Messi to thank as the Argentina forward took his season tally to 10 goals in seven games courtesy of a devastating 10-minute spell at Camp Nou.
In the other group match, there was far less excitement as Celtic created little at Parkhead in a 0-0 draw with Benfica.
Manchester United made a good start following midfielder Michael Carrick's early goal, but failed to impress in a 1-0 win against Galatasaray. Portugal winger Nani missed a second-half penalty as United struggled to get going at Old Trafford.
The Turkish side can consider itself unlucky, hitting the goal-frame three times, having two penalty appeals rejected and forcing a couple of good saves from David de Gea.
Romanian side CFR Cluj moved top of Group H after winning 2-0 at Braga from two first-half goals by Brazilian midfielder Rafael Bastos, who was once rejected by the Portuguese side.
Bayern Munich, last season's runner-up, missed a late penalty in its 2-1 win against Valencia in Group F.
Bayern midfielder Bastian Schweinsteiger opened the scoring in the 38th minute and teammate Toni Kroos' powerful long-range strike gave the home side some breathing space.
Valencia substitute Nelson Valdez set up some late drama with an injury-time header, and there was still time for Bayern forward Mario Mandzukic to miss a penalty on his Champions League debut.
Belarusian champion BATE Borisov won 3-1 at Lille in the other Group F match, stunning Lille through a slick display of counterattacking with former Arsenal midfielder Aleksandr Hleb pulling the strings.
Midfielder Aleksandr Volodko, striker Vitali Rodionov and midfielder Edgar Olekhnovich scored in the first half. Center back Aurelien Chedjou pulled a goal back on the hour mark for the dispirited home side, which failed to progress from the group stage last season.
AP