Daniel Sturridge sent Liverpool top of the Premier League with a 1-0 win over Manchester United on Sunday, while Arsenal clipped Tottenham Hotspur's wings in the north London derby.New United manager David Moyes was without Wayne Rooney due to a head injury that looks set to rule him out of England's World Cup qualifiers and in his absence, the Scot's poor record at Anfield continued.Sturridge, who could benefit from Rooney's absence for England against Moldova and Ukraine, scored the only goal in the fourth minute, having also been the match-winner in 1-0 wins over Stoke City and Aston Villa.It means that Liverpool are the only team to have won their opening three fixtures, after big-spending Spurs lost 1-0 at Arsenal later in the day."It is a great win for our belief," said Liverpool manager Brendan Rodgers."Last season we drew too many of the big games and we lost both times to Manchester United, but today was another marker for us and since January our form has been very, very good."Although the season remains young, it was a painful defeat for United, who already trail their old rivals by five points."I thought we played really well," said Moyes, the former Everton manager, who revealed after the game that Rooney could be out for three weeks."We had long periods of the game, but couldn't score. Apart from the lapse in concentration for their goal, we played well."We got two or three opportunities but it was unfortunate we didn't take them."The game was preceded by a minute's applause for the late Bill Shankly, who would have turned 100 on Monday, and the legendary former Liverpool manager would have appreciated his side's purposeful start.There were less than four minutes on the clock when Liverpool struck, with Sturridge stepping off the line to glance Daniel Agger's header past David de Gea and mark his 24th birthday with an 11th goal in nine games.The visitors improved in the second half, but Liverpool goalkeeper Simon Mignolet repelled a Ryan Giggs header and a rasping drive from substitute Nani before Robin van Persie slashed a late chance wide.The final whistle drew roars from the home fans, but there was concern for watching England manager Roy Hodgson, who saw both United defender Phil Jones and Liverpool right-back Glen Johnson hobble off with injuries.At the Emirates Stadium, Spurs included new record signing Erik Lamela on the bench; the star recruit of a close-season splurge in which they have spent around £110 million ($170 million, 129 million euros) on new players.It was a familiar combination that saw Arsenal take a 23rd-minute lead, however, with Theo Walcott crossing for Olivier Giroud to beat France teammate Hugo Lloris with an exquisite near-post finish.Mathieu Flamini, who has returned to the club from AC Milan, made his second Arsenal debut as a substitute for Jack Wilshere, but fears about the injury-prone England midfielder's fitness were allayed by the news he had only been suffering from stomach cramps.After Lloris's fingertips prevented Giroud from doubling Arsenal's lead in the second half, Spurs manager Andre Villas-Boas sent on Lamela and Sandro, who came on after an injury to Etienne Capoue.Roberto Soldado vainly appealed for handball after his shot was blocked by Giroud, but while Nacho Monreal was unable to add a second after Lloris saved from Walcott, it did not stop Arsene Wenger's side stealing into the top four at Spurs' expense."To sum it up, their goalkeeper was their best player," Arsenal manager Wenger told Sky Sports."We had plenty of chances, but I concede that we did hang on in the end because we just wanted to keep the score."