The England international had only been on the pitch five minutes when his 25-yard drive beat goalkeeper Jerzy Dudek with the aid of a deflection.

It was a severely harsh blow for Liverpool, who were denied at least one blatant penalty in a game they controlled for long periods before Cole claimed the winner against them for the second time this season.

A frustrating afternoon for Liverpool was compounded by a bad injury for Spanish midfielder Xabi Alonso, who was left nursing a broken ankle after a dreadful challenge by Frank Lampard.

The England midfielder was fortunate to escape with just a caution. Alonso, who cost the Merseyside club 10.5 million pounds when he joined from Real Sociedad in the summer, is expected to be out of action for the next two months.

The Merseyside club were looking to extend a three-match winning run, their best Premiership form since Rafael Benitez took charge in the summer.

Leading scorer Milan Baros was once again missing with a hamstring injury as Liverpool looked to become only the second Premiership side to defeat Chelsea.

Jose Mourinho's side arrived at Anfield protecting an 11-match unbeaten record in the league. Only three clubs -- Aston Villa, Manchester City and Tottenham Hotspur -- had prevented them from scoring while they had not conceded a goal in more than five hours of action.

Yet Czech Republic goalkeeper Petr Cech was forced to come to his side's rescue on more than one occasion during a lively first half in which Liverpool, who carved out the better chances, were denied a 37th minute penalty after Tiago clearly handled the ball inside his own area.

Chelsea appeared to be suffering from a New Year hangover as French defender Djimi Traore, who has not scored a league goal in almost six years at Anfield, had a 15th minute drive saved after Eidur Gudjohnsen had lost possession deep inside his own half.

The visitors defence was again caught napping four minutes later as John Arne Riise delivered a fine cross which would surely have resulted in a goal had Alonso arrived inside the six-yard area a fraction earlier.

Alonso's involvement ended in the 27th minute when he limped off six minutes after Lampard's cynical challenge. X-rays confirmed he had fractured a bone in his ankle.

Steven Gerrard, who Chelsea tried to sign last summer, Luis Garcia and substitute Antonio Nunez all forced Cech into saves before the interval, although Liverpool were given a warning when Tiago's through ball sent Arjen Robben clean through only for the Holland striker to be denied by a splendid save by Jerzy Dudek.

Controversy flared eight minutes before the break when Tiago handled inside his own area as Nunez attempted a header but the incident was missed by referee Mike Riley who was surrounded by incensed Liverpool players.

Liverpool continued to press with Jamie Carragher hitting the roof of the net from distance while Gerrard also went close before Cole had the final say after Robben's corner had been headed into his path by Glen Johnson.

It was Cole's fourth goal of the campaign. The England midfielder also scored the winner when the two sides met at Stamford Bridge in October.