Chelsea kept their Premier League title hopes alive with a 1-0 victory over Middlesbrough on Sunday but their performance would have caused few alarms for leaders Manchester United [Images].

Also read: Arsenal, Man U win

Ricardo Carvalho's well-placed header inside the opening six minutes at Stamford Bridge proved sufficient for Avram Grant's side to close the gap to five points but they rode their luck after the break.

Boro's Brazilian striker Afonso Alves, still to find the net since signing for 12 million pounds ($23.98 million) in January, twice hit the woodwork after coming on as a substitute while defender David Wheater also headed against the bar.

Chelsea, unbeaten at home in the league for four years, survived a nervy final 25 minutes to move back above Arsenal [Images] into second place with 71 points from 32 games to United's 76.

However their display did little to suggest they will be able to close the gap in the six games they have left, one of which is against United at home.

"It was important to win at this stage of the season but the quality was not there today," manager Avram Grant told Setanta Sports. "Maybe we scored too early. We didn't play our game and sometimes there is no reason for it."

Carvalho's powerful header from Wayne Bridge's free kick suggested an easy afternoon for Chelsea but Didier Drogba [Images], Joe Cole and Shaun Wright-Phillips all wasted good chances to put the result beyond doubt.

Alves was introduced after 64 minutes and he should have equalised almost immediately when he headed wide from virtually in front of Carlo Cudicini's goal.

With 20 minutes to go a dreadful error of judgement by Cudicini gifted Alves the ball 25 metres out with an empty goal gaping, but this time his curled shot bounced back off the post.

Alves continued to worry Chelsea's defence and sent a header against the bar. The ball came out to Wheater, who also sent his effort against the woodwork.

Middlesbrough drop to 13th place, below Newcastle United who eased their relegation fears with a 4-1 victory at Tottenham Hotspur after trailing 1-0. Nicky Butt, Geremi, Michael Owen [Images] and Obafemi Martins were all on target.

Later on Sunday, Liverpool took on Everton in the Merseyside derby, with both sides battling for fourth place.

Fernando Torres scored as early as the seventh minute, with a right footed shot from the centre of the box, and that was the difference between the two neighbours in the final analysis.

Rafa Benitez's side got the full three points and moved clear fourth. Liverpool now have 62 points from 32 games, five more than Everton with the latter having also played the same number of games.