LONDON5 - Manchester City and Liverpool, last season's top two in the Premier League, were both made to sweat by determined opposition before opening their campaigns with hard-fought victories on Sunday. David Silva and Sergio Aguero scored as champions City began their title defence with a 2-0 success at Newcastle United, after Daniel Sturridge had struck late in the game to earn Liverpool a 2-1 win at home to Southampton.The two rivals joined five other teams, including Arsenal, on maximum points, ahead of their showdown at the Etihad Stadium a week on Monday in the first major head-to-head of the season. "It was very important for us to start with a win," said City manager Manuel Pellegrini. "We talked to the squad about the 'two h's' -- we were hungry and humble. We need both if want to continue winning titles and improve on what we did last season. We didn't have any clean sheets in pre-season, but we were very solid in this game."Pellegrini gave a debut to new Brazilian midfielder Fernando and saw his side take the lead in the 38th minute at St James' Park. Yaya Toure found Edin Dzeko with a lofted pass over the top and as Newcastle's centre-backs rushed across, the Bosnian teed up Silva with a clever back-heel and the Spain midfielder coolly beat Tim Krul. Newcastle, who handed debuts to Daryl Janmaat, Jack Colback, Remy Cabella and Emmanuel Riviere, improved after the interval, with Cabella and Paul Dummett spurning opportunities to hit the target.Newcastle substitute Ayoze Perez then saw a curling effort deflected agonisingly wide by Fernando, before Aguero ran through and beat Krul at the second attempt in stoppage time to finally put the game to bed. Earlier, Sturridge snaffled a 79th-minute winner as Liverpool edged Southampton at a sun-soaked Anfield. Raheem Sterling put Liverpool ahead midway through the first half, but Nathaniel Clyne lashed home an equaliser shortly before the hour following a neat exchange with debutant Dusan Tadic.Brendan Rodgers's Liverpool looked destined to drop points in their first competitive game since the sale of Luis Suarez to Barcelona, but with 11 minutes to play, Sterling teed up Sturridge to flick home the winning goal. "We scored two very good goals and we're delighted about the win," Liverpool manager Rodgers told Sky Sports. "In terms of the character and desire and the will to win, we were exceptional."With debutants Javier Manquillo and Dejan Lovren -- the former Southampton defender -- in their starting XI, Liverpool dominated possession in the early stages and took the lead in the 23rd minute. The goal owed much to the tenacity and vision of Jordan Henderson, who helped Manquillo dispossess Tadic, won a 50-50 with Morgan Schneiderlin, and then freed Sterling to beat Fraser Forster with a first-time finish.It was a turbulent close season for Southampton, who lost five key players and appointed a new manager in Ronald Koeman, but they were not cowed by Liverpool's opener and equalised in the 56th minute. Clyne rolled a pass forward to Tadic and the Serbian held off his marker before backheeling the ball into the path of his onrushing team-mate, who thrashed a shot into the top-right corner.After Steven Davis had shot meekly at Liverpool goalkeeper Simon Mignolet, Sterling headed on a loose ball for England team-mate Sturridge to nudge home the winner from a matter of yards. There was time for one last scare for Liverpool, with Mignolet touching a drive from Schneiderlin onto the bar and Southampton debutant Shane Long -- a late substitute -- heading the rebound wide.Manchester United's campaign got off to a false start on Saturday when they lost 2-1 at home to Swansea City in new manager Louis van Gaal's first competitive game. Arsenal, meanwhile, needed an injury-time goal from Aaron Ramsey to overcome Crystal Palace 2-1. Chelsea, who finished third last season, open their campaign at promoted Burnley on Sunday.