LONDON — Liverpool's dream of a first title in 24 years moved closer to reality after a 3-2 win at lowly Norwich City Sunday opened up a five-point lead over second-placed Chelsea with three matches remaining. Arsenal beat Hull City 3-0 in a dress-rehearsal for next month's FA Cup final to stay one point ahead of Everton, who beat Manchester United 2-0 on David Moyes's return to Goodison Park, in the race for fourth spot. Two Raheem Sterling goals and Luis Suarez's 30th league strike of the season helped Liverpool to its 11th consecutive Premier League victory and confirmed its place in the Champions League next season. It moved to 80 points, five ahead of Chelsea which suffered a shock 2-1 defeat by bottom club Sunderland Saturday. Third-placed Manchester City, on 71 points and with two matches in hand, plays West Bromwich Albion Monday. Liverpool has not won the title since 1990, two years before the Premier League began, and can move to the brink of ending that drought when it meets Chelsea at Anfield next Sunday. Sterling put the Reds ahead after four minutes when he received the ball from Suarez, shifted right and unleashed a shot from outside the box that grazed Michael Turner, giving John Ruddy no chance. He turned provider for the second on 11 minutes when he sent in a low cross and Suarez placed the ball inside the far post to become the first Liverpool player since Ian Rush in 1986-87 to score 30 league goals in a season. Norwich pulled one back after the break through Gary Hooper, but Sterling restored Liverpool's buffer with another deflected effort before Robert Snodgrass ensured a nervous last 13 minutes with a second for the hosts. Arsenal took the lead after a neat passing move involving Mesut Ozil and Santi Cazorla allowed Ramsey to steer the ball home after 30 minutes, his first goal since November having missed three months through injury. Podolski doubled Arsenal's lead on 45 minutes, volleying in after Ramsey's chested layoff from Olivier Giroud's cross and the German scored his fifth in as many matches after the break, following up after Steve Harper had blocked Ramsey's effort. Arsenal stayed one clear of Everton, which ensured Moyes suffered an unhappy return to the club he managed for 11 years, with defeat also confirming seventh-placed United cannot qualify for the Champions League. Everton was awarded a penalty when Phil Jones put his arm in the way of Romelu Lukaku's thunderous shot and Leighton Baines drilled the penalty down the middle on 28 minutes. Kevin Mirallas doubled the lead just before the break, finishing from a tight angle. United failed to muster a shot on goal in the first half, a fact acknowledged by Moyes, who was not asked in a television interview about his return to Goodison. Leverkusen, Stuttgart claim vital Bundesliga wins Bayer Leverkusen reclaimed fourth place in the Bundesliga with a 4-1 with at relegation-threatened Nuremberg and Stuttgart eased its relegation fears with a 3-1 win over Schalke Sunday. Martin Harnik scored twice for Stuttgart to move four points clear of Hamburger SV in the relegation play-off place. The Austrian striker opened the scoring with a header from Daniel Didavi's well-delivered free kick in the 23rd. Cacau scored in the 54th. Five minutes later, Gotoku Sakai breezed past Kaan Ayhan to set up Harnik for Stuttgart's third. Adam Szalai pulled back what proved to a consolation in the 69th. Sociedad prevails Carlos Vela skillfully chested down a long pass before firing in Real Sociedad's injury-time winner to snatch a dramatic 2-1 win at home over Espanyol in the Spanish league Saturday. Vela's 13th goal in league play allowed Sociedad to rise into provisional sixth place, and moved the Basque club closer to clinching a Europa League berth. Also, Valencia forward Jonas went on in the second half and scored to secure a 1-1 draw at Osasuna, while Getafe stayed in the drop zone after a 0-0 draw at Levante. — Agencies