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Chelsea's spot in the last 16 was already assured while APOEL could have jumped above Atletico Madrid - who lost 3-0 at home to Porto - and into the Europa League, had they won.
First-half goals from Michael Essien and Didier Drogba cancelled out an early opener from Marcin Zewlakow.
But, despite numerous opportunities in the second half, the expected home win did not materialise and, when Jon Obi Mikel dallied late on, Mirosavljevic nipped in to finish low past stand-in goalkeeper Ross Turnbull.
Encouraging performances from Gael Kakuta and Fabio Borini notwithstanding, a faltering defence will give cause for concern for Chelsea boss Carlo Ancelotti, with his once watertight backline having shipped seven goals in a three-match winless run.
The Italian will also have to do without the services of goalscorer Essien for the foreseeable future after the midfielder sustained a hamstring injury in the first half.
APOEL stunned the home supporters with their sixth-minute opener. Zewlakow became the first player since Hull's Stephen Hunt on the opening day of the Premier League season to score a goal at Stamford Bridge when he finished well following a pass from Constantinos Charalambidis.
The visitors had previously come close when a well-worked free-kick gave a shooting opportunity to Joost Broerse but the defender's turn and shot was straight at Turnbull.
A bright start from the Cypriots threatened to embarrass Ancelotti's much-changed team but Joe Cole had a header ruled out for offside shortly before Essien levelled legitimately in the 19th minute.
The Ghanaian unleashed a fierce shot from 25 yards that swerved beyond the flailing Dionissis Chiotis.
It proved to be the midfielder's last significant involvement with a hamstring injury sustained three minutes later curtailing his evening's work and possibly also his Christmas commitments.
Chelsea had not got substitute Frank Lampard on the pitch before they took the lead through Drogba.
Everything the Ivorian hits at the moment seems to end in a goal and so it was when Kakuta and Yuri Zhirkov combined down the left and the latter cut the ball back to the striker 10 yards from goal. The finish, low and into the bottom corner, was unerring.
More bright play from Kakuta gave a shooting chance to Cole but the England international's effort was too close to Chiotis.
Kakuta has so far made headlines for all the wrong reasons. His signing is the reason why Chelsea are appealing a transfer ban, while he also missed the decisive penalty in a Carling Cup shoot-out defeat to Blackburn last week.
Against APOEL, the 18-year-old Frenchman showed plenty of promise. Kakuta was again the architect for another Cole chance at the start of the second half.
Turnbull had to drop on a shot from Nuno Morais but most of the action was at the opposite end of the pitch.
Drogba hit a free-kick he won himself but the ball dipped narrowly over, while Cole had a shot deflected over the bar.
Kakuta was replaced by Fabio Borini 17 minutes from the end as Ancelotti sought to run the rule over another of the club's youngsters. The Italian, like his French predecessor, impressed during his brief spell on the pitch.
It was one of the Blues' more experienced players, Mikel, who was the cause of his team's downfall three minutes from full-time. A needless loss of possession to Mirosavljevic ushered in the Serbian substitute to finish with a low shot underneath Turnbull.
Top spot in Group D already assured, the loss of two points will not unduly worry Ancelotti but the Italian will want his team to return to their more miserly ways in time for this competition's more testing engagements.
Chris Stanton / Eurosport
source: http://uk.eurosport.yahoo.com/08122009/58/champions-league-late-leveller-denies-blues.html
