Robin van Persie's late penalty earned below-par Manchester United a 2-1 victory over 10-man Liverpool in an emotionally-charged Premier League clash at Anfield and champions Manchester City were held to a 1-1 home draw by Arsenal on Sunday.
United's prolific Dutchman sealed the points when he fired his spot-kick past the despairing dive of Pepe Reina after Glen Johnson had brought down Antonio Valencia.
Despite being well below their best, United moved into second spot with 12 points, one point behind leaders Chelsea.
City drew for third time in their opening five games, Laurent Koscielny equalising late for Arsenal after Joleon Lescott had headed the hosts into a halftime lead.
Both sides are unbeaten with nine points.
Tottenham Hotspur have eight after Jermain Defoe scored the winner in a 2-1 victory over Queens Park Rangers, Spurs's first home win under new manager Andre Villas-Boas.
Demba Ba scored in a 1-0 win for Newcastle United over their former manager Chris Hughton's Norwich City.
The first match at Anfield since this month's Hillsborough report cleared Liverpool's fans of blame for the deaths of 96 of supporters at the 1989 FA Cup semi-final sparked into life after 39 minutes when Jonjo Shelvey was red-carded.
However, Liverpool deservedly went ahead straight after halftime through Steven Gerrard's volley, only for United to hit back six minutes later through a curling effort by fullback Rafael.
Van Persie's late strike, his fifth league goal of the season, left Liverpool manager Brendan Rodgers still awaiting his first league win of the season after five games, the club's worst start to a Premier League campaign.
Photograph: Michael Regan/Getty Images