Daniel Sturridge made it three goals in three games - all in 1-0 victories - to send the Reds top of the Premier League table with a flawless record of three wins to start the season for the first time since 1994.
The 24-year old England striker glanced home a header from close range after Daniel Agger had nodded Steven Gerrard's corner goalward, giving Liverpool the lead in the fourth minute, which they held onto for the entirety.
The win has Brendan Rodgers' men sitting on nine points, two ahead of second-placed Chelsea, who were not involved in league action this weekend because of Friday's UEFA Super Cup which they lost to Bayern Munich in penalties following a 2-2 draw after extra-time. David Moyes' United find themselves seventh.
Manchester City are sitting in third spot thanks to their 2-0 home victory over Hull City which came courtesy of a 65th minute header from summer signing Alvaro Negredo and a fabulous 90th minute free-kick from Yaya Toure.
City are level on six points with fourth-placed Arsenal who got the better of Tottenham with a 1-0 win in the North London derby at the Emirates Stadium on Sunday.
French striker Olivier Giroud, like Sturridge, made it three goals in three outings when he cleverly prodded home Theo Walcott's cross to the near post in the 23rd minute which enabled the Gunners to record a second lot of three points over London rivals in two weeks following their 3-1 triumph at Fulham.
Elsewhere, Newcastle United logged their first win of the season with a 1-0 home result over Fulham thanks to a moment of individual brilliance from Hatem Ben Arfa who scored with a wonderful effort form the edge of the area in the 86th minute.
Nathan Redmond scored his first goal for Norwich City in fine style as they defeated Southampton 1-0 at Carrow Road, cutting in from the left before firing home from outside the box, as substitute Jermaine Pennant's 82nd minute goal from a free-kick gave Stoke City a 1-0 win at West Ham United. It was his first goal since May 2011
Top flight returnees Crystal Palace shocked ten-man Sunderland 3-1 at Selhurst Park with Danny Gabbidon, Dwight Gayle (penalty) and Stuart O'Keefe all on target as Cardiff City and Everton played out a 0-0 draw at the Cardiff City Stadium.
To wrap it up, Swansea City grabbed a 2-0 win over West Bromwich Albion at The Hawthorns thanks to goals either side of the break from Ben Davies and Pablo Hernandez for the first victory of the campaign which left the Baggies at the foot of the table.
2013/14 Barclays Premier League scores