Vibrant Shakhtar sink European champions Chelsea

(CNN) -- A year to the day after racially abusing an opponent, John Terry stepped out as Chelsea captain wearing an anti-racism armband -- only for the Blues to suffer their first Champions League defeat since winning the trophy in May.

Terry wore the band as part of a week of action organized by the group 'Football Against Racism in Europe (Fare)', which has asked all club captains in European competition to help its campaign.

The 31-year-old is currently serving a domestic ban after being found guilty of racial abuse against Anton Ferdinand by the English FA -- but his suspension does not apply to European football, where Chelsea were subjected to a torrid time by Shakhtar Donetsk.

Read: Terry waives FA racism appeal

Unbeaten over the last 11 months, the Ukrainian champions won 2-1 after Alex Teixeira gave the hosts the perfect start with a goal after three minutes as the ball ricocheted off Terry into his path.

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Shakhtar would have added to their lead but for some fine goalkeeping from Petr Cech and had to wait until the 52nd minute before Fernandinho rewarded their dominance with a deserved second goal.

Late on, Oscar became the third Brazilian to score in the European tie but his close-range strike was too little too late as Chelsea lost their first Champions League game since going down 3-1 in Italy against Napoli in February.

"Perhaps it was one of our best games in recent times," Shakhtar coach Mircea Lucescu told the official website of European body UEFA. "And I have to say that this Chelsea side are stronger than the one that won the Champions League last season. That makes our victory even more important."

Chelsea stay second in Group E after two-time winners Juventus could only draw 1-1 at the Danish home of tournament new boys Nordsjaelland.

Elsewhere, Barcelona and Manchester United both came from behind as they struggled to beat less fancied opposition despite boasting home advantage.

Deprived of some key personnel in defense, Barca were stunned when Scottish visitors Celtic took the lead through Giorgios Samaras' deflected header -- only for Andres Iniesta to draw the four-time champions level just before the break with a fine goal.

After outstanding Celtic goalkeeper Fraser Forster thought he had done enough to repel the home side's best efforts, Barcelona secured their 100th Champions League win when Jordi Alba found the net four minutes into stoppage time to secure a 2-1 win.

In England, Manchester United were equally surprised as Brazil's Alan gave Portugal's Braga a two-goal lead within 20 minutes inside a shocked Old Trafford.

Mexican striker Javier Hernandez made the most of a rare start as he reduced the deficit shortly moments later, before wrapping up the win 15 minutes from time after Jonny Evans had scrambled home an equaliser shortly after the hour.

"It's been the story of our season at home -- start badly, lose goals and have to fight back to rescue games," said United coach Alex Ferguson after the 3-2 victory. "Some of our football was fantastic but conceding so many goals is a concern."

Elsewhere, Spartak Moscow won their first match and points in Group G, beating Portuguese side Benfica 2-1 in Russia to trail Barca by six points and Celtic by just one.

Spaniards Valencia were the biggest winners of the night, winning 3-0 in Belarus to bring home side Bate Borisov -- who stunned Bayern Munich 3-1 in their last European game -- back down to earth.

Meanwhile, the Germans, who were beaten runners-up on home soil against Chelsea in the final in May, rebounded in solid if unconvincing fashion when winning 1-0 at French side Lille.

Galatasaray could not profit from playing against a CFR Cluj side reduced to ten men for over an hour as the Turks conceded an own goal and missed a penalty before equalizing late on to draw 1-1.