Juan Mata scored on his Chelsea debut in a 3-1 home win over promoted Norwich City while Jordan Henderson and Charlie Adam netted their first Liverpool goals in another 3-1 triumph over Bolton Wanderers on Saturday.
The victories gave the two big-spending sides seven points from three matches and pushed them to the top of the Premier League table alongside Wolverhampton Wanderers, who drew 0-0 at Aston Villa.
At the other end of the table Blackburn Rovers remain bottom without a point after Junior Hoilett and Mauro Formica missed penalties in a 1-0 home defeat by Everton who prevailed when Mikel Arteta made no mistake with his injury-time spotkick.
Last season's runners-up Chelsea have failed to sparkle in the early weeks of the campaign but Portuguese full back Jose Bosingwa gave them a superb early start with a rare goal from 22 metres.
Norwich equalized in comical fashion when stand-in goalkeeper Hilario dropped a cross and Grant Holt hooked the ball into an empty net midway through the second half but the hosts went ahead again through Frank Lampard's 82nd-minute spotkick.
The penalty was awarded after Norwich goalkeeper John Ruddy was dismissed for bringing down Ramires.
Spanish substitute Mata, who signed from Valencia this week, then exposed Norwich's 10 men when he bent in a third goal during 11 minutes of injury time.
"Dream debut! First game, victory and first goal. I cannot ask for more. Very happy and now to enjoy the moment and think about the national team," winger Mata said on Twitter ahead of Spain's friendly against Chile on Friday and a Euro 2012 qualifier against Liechtenstein four days later.
The long stoppage time came after Chelsea's Didier Drogba, brought in to partner Fernando Torres up front, was knocked unconscious and had to have extensive treatment on the pitch.
The Ivorian was taken to hospital before being released later.
Liverpool took the lead after 15 minutes against Bolton when former Sunderland midfielder Henderson sent Anfield into raptures with a coolly-taken strike following superb play by Luis Suarez, preferred up front to Andy Carroll.
The Uruguayan's chip on to the bar later on was perhaps overly ambitious but Liverpool's win was never in doubt once Martin Skrtel headed in Adam's corner before the former Blackpool midfielder drove home a crisp right-footed shot.
Ivan Klasnic netted a late consolation.
Like United and City, Wolves had won their opening two fixtures but were content to leave Villa with a point after the Birmingham-based side put their local rivals under pressure for long spells.
Gabriel Agbonlahor had the best chance for the hosts but goalkeeper Wayne Hennessey pulled off a good save.
Argentine Franco Di Santo scored twice to give Wigan Athletic a 2-0 home win over promoted Queen's Park Rangers with the visitors deciding not to give Joey Barton a debut after his move from Newcastle United.
Villa and Wigan are joint sixth.
Promoted Swansea, still looking for their first Premier League goal, drew 0-0 with Sunderland in south Wales in a game where both sides hit the bar.