LONDON, March 30: 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.

Ricardo Carvalho’s well-placed header inside the opening six minutes at Stamford Bridge proved sufficient for Avram Grant’s side to cut the gap to five points but they rode their luck as Boro’s Brazilian striker Afonso Alves twice hit the woodwork.

Liverpool later completed a quartet of weekend wins for the top four with a 1-0 defeat of Everton at Anfield. The result tightened their grip on fourth place, which is worth a slot in the Champions League qualifiers.

Spaniard Fernando Torres scored his 21st league goal of the season to defeat a subdued Everton side, who now look destined for a UEFA Cup place.

Chelsea, unbeaten at home in the league for four years, survived a nervy second half to move back above Arsenal into second place with 71 points from 32 games while United, 4-0 winners against Aston Villa on saturday, have 76.

Arsenal, who beat Bolton Wanderers 3-2 on Saturday, have 70 points, with Liverpool back on 62 and Everton on 57.

Chelsea’s stuttering 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.

Carvalho’s powerful header from Wayne Bridge’s free kick suggested an easy afternoon for Chelsea but Didier Drogba, 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 dropped 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 and Obafemi Martins were all on target.

Everton arrived at Anfield with genuine hopes of overtaking their city rivals but produced a stale performance and barely had a worthwhile effort on goal.

The game was only seven minutes old when Torres he fired a clinical shot across keeper Tim Howard into the net.

Liverpool, who face Arsenal in the Champions League quarter-final, first leg on Wednesday, were dominant throughout.

Meanwhile, Wayne Rooney scored twice in the second half and Cristiano Ronaldo played a part in all four goals to help Manchester United crush Aston Villa 4-0 on Saturday.

United also netted in the first half with a cheeky Ronaldo back-heel and a header from Carlos Tevez.

Arsenal, down to 10 men for an hour, ended a six-year league jinx at Bolton Wanderers as they fought back from two goals down for a 3-2 win.

At Old Trafford, where the second half was played in pouring rain, the league’s top scorer Ronaldo took his tally for the season to 26 when he struck in the 17th minute.

A cross was poorly cleared and the loose ball fell to the Portugal striker who, with his back to goal, flicked it with his left heel through defender Martin Laursen’s legs and past keeper Scott Carson.

Tevez made it 2-0 just past the half hour. Ronaldo flicked on a Ryan Giggs pass for Rooney to take the ball round Carson for the third in the 53rd minute, his first goal in eight games.

Rooney added the fourth in the 70th minute.

Midfielder Matthew Taylor put Bolton two up in the first half with goals either side of the dismissal of Arsenal’s Abou Diaby for a high tackle on Gretar Steinsson.

Captain William Gallas led Arsenal, who had not won at the Reebok Stadium in their previous five league visits and had lost on their last three, back into the match when he turned in Cesc Fabregas’s corner in the 63rd minute.

Robin van Persie equalised with a penalty five minutes later after Gary Cahill brought down Alexander Hleb and an own goal by Jlloyd Samuel following Fabregas’s 90th-minute shot ended Arsenal’s run of five league games without victory.

Derby County were relegated after a 2-2 draw at home to Fulham, Birmingham City’s 3-1 win over Manchester City sealing the bottom team’s fate.

Results:

Played on Sunday:

Chelsea 1 Middlesbrough 0

Liverpool 1 Everton 0

Tottenham Hotspur 1 Newcastle United 4

Played on Saturday:

Birmingham City 3 Manchester City 1

Bolton Wanderers 2 Arsenal 3

Derby County 2 Fulham 2

Manchester United 4 Aston Villa 0

Portsmouth 2 Wigan Athletic 0

Reading 0 Blackburn Rovers 0

Sunderland 2 West Ham United 1

—Reuters