LONDON (AFP) - Luiz Felipe Scolari has warned Chelsea's title rivals that his side are not at full power yet despite their convincing 3-1 win at Manchester City. Scolari has had to cope with injuries to key players like Michael Essien and Michael Ballack and the Blues boss knows his side will get much stronger when he can finally choose a settled team. Despite those problems, Chelsea are already top of the table and six points ahead of reigning champions Manchester United who lost 2-1 at bitter rivals Liverpool. Even when Robinho put City into the lead at a buoyant Eastlands on Saturday, Scolari's side never looked flustered. They hit back to give big-spending City a reality check thanks to goals from Ricardo Carvalho, Frank Lampard and Nicolas Anelka. "We have improved because we have had many problems from when we started until now," Scolari said. "I have had to put player A, B or C in the team and they try to do their best. For the coach that is important. We will keep getting better." Robinho, making his debut, took only 13 minutes to show why City paid 32.5 million pounds to persuade the Brazilian to snub Chelsea as he whipped a free-kick over the wall and past Petr Cech. But City's lead was shortlived. Just three minutes later John Terry's header deflected to Carvalho and the Portugal defender smashed home. Chelsea pushed City back after that and Lampard scored on 53 minutes when he finished an incisive move with a fine low strike. Anelka's 69th minute goal put the result beyond doubt despite Terry's late red card for a professional foul on Jo. Earlier, Liverpool finally got the better of Manchester United as Ryan Babel's late goal clinched a 2-1 win over the European champions. Rafa Benitez's side had lost seven of the last eight league encounters with their rivals dating back to 2004, and the Reds fell behind at Anfield when Carlos Tevez struck for United in the third minute. But Wes Brown's own goal gave Liverpool a 27th-minute equaliser and Babel, on as a substitute just six minutes earlier, grabbed the decisive goal 13 minutes from full-time. The day got even worse for Sir Alex Ferguson when Serbian defender Nemanja Vidic was sent off in stoppage time for a crude elbow on Xabi Alonso. "It is good for the confidence of the players," Benitez said. "At half-time we were talking about having confidence and determination going forwards - and in the second half we were the best team." United boss Ferguson added: "You don't expect that from Manchester United. Liverpool produced a performance of tackling, hassling and getting about us. Overall they were the better team." The hangover from Kevin Keegan's departure took its toll on Newcastle as the managerless Magpies crashed to a 2-1 defeat against Hull at St James' Park. Thousands of Newcastle fans protested against owner Mike Ashley and director of football Dennis Wise before the first match since Keegan's resignation and then saw their team produce a woeful performance. Marlon King struck from the penalty spot after Nicky Butt's 34th minute foul on Peter Halmosi. Newcastle conceded a second in the 55th minute when King drove home. Xisco pulled one back on his debut, but it was too late to save Newcastle, who had Danny Guthrie sent off in the last minute. Arsenal, inspired by Togo striker Emmanuel Adebayor's hat-trick, thrashed Blackburn 4-0 at Ewood Park. Robin van Persie slotted him in the eighth minute and Adebayor put Arsenal in control on the stroke of half-time. He claimed the third from the penalty spot in the 81st minute and completed his treble in stoppage time. West Ham's new manager Gianfranco Zola watched from the stands as his side crashed to a 3-2 defeat at West Bromwich Albion. James Morrison gave Albion the perfect start in the third minute. But Zola, who won't officially take charge until next week, saw Mark Noble equalise in the 29th minute. Lucas Neill put West Ham ahead in the 35th minute but Roman Bednar levelled with a penalty two minutes later before Chris Brunt grabbed an 83rd minute winner for Albion. Jermain Defoe's second half double gave Portsmouth a 2-1 victory against Middlesbrough at Fratton Park. Mido struck for Middlesbrough in the 24th minute but Defoe finished off Peter Crouch's pass to level after 59 minutes and snatched the winner four minutes from the final whistle. Fulham's newboys combined to set up a 2-1 win over Bolton at Craven Cottage. Zoltan Gera, a close-season signing from West Bromwich, put Fulham in front in the 15th minute and Bobby Zamora, who joined from West Ham, doubled their lead just before half-time. Kevin Davies's 82nd minute strike was no consolation for Bolton. Amr Zaki's blistering start to life with Wigan continued as the Eygpt striker's fifth goal of the season rescued a 1-1 draw against Sunderland. Titus Bramble's early own goal gave Sunderland the lead at the JJB Stadium. But Zaki, a pre-season loan signing from El Zamalek, equalised in the 78th minute before Sunderland's Lee Cattermole was sent off in the closing minutes.