Bill Shankly's name reverberated around Anfield before and after a fitting occasion to fall on the eve of what would have been his 100th birthday. The Liverpool performance in between was too backs-to-the-wall to represent a tribute in his image. It did not matter. "If you are first, you are first. If you are second, you are nothing," Shankly once said, and first always tastes sweeter in these parts at the expense of Manchester United.

An early goal from Daniel Sturridge on his 24th birthday maintained Liverpool's 100% start to the Premier League season, their best since 1994, and preserved David Moyes's winless record at Anfield in the process. It is now 13 visits to the red side of Stanley Park without a victory for the United and former Everton manager and this time his thin excuse of working with fewer resources than Liverpool was redundant.

Liverpool's bench was full of inexperienced youthful promise. Moyes could throw on Antonio Valencia, Nani and Javier Hernández but could not arrest a careless and unimaginative display from the visitors, who dominated possession but toiled in the final third. Robin van Persie was particularly off-key.

Shankly's maxim clearly holds little weight with his compatriot in the United dug-out. "I thought we played very well," Moyes argued. "We gave away a bad goal in the opening few minutes but with the exception of that it was probably the best we've played this season." The observing Roy Hodgson once said a similar thing after a lame Liverpool defeat at Goodison Park and fooled no one. Beyond argument this is United's worst start to a season in five years and, on this evidence, Everton's chairman, Bill Kenwright, should hold his old friend to ransom over Marouane Fellaini.

With Wayne Rooney on the sidelines with a head injury "for a few weeks", according to Moyes, Van Persie enduring an off-day and Danny Welbeck ineffective, United failed to disturb a commanding Liverpool defence. One-nil wins are becoming a habit for Brendan Rodgers' team in the league – this was their third in three – but the defensive resilience on show was vastly superior to previous outings.

It was inspired from the front, a time-honoured Liverpool tradition, by the impressive Sturridge and encapsulated by imperious central defenders, Daniel Agger and Martin Skrtel. Considering Skrtel was brought in from the cold only because of an injury to Kolo Touré, his focus and professionalism were outstanding. With Tiago Ilori, Mamadou Sakho and Victor Moses present before their proposed moves from Sporting Lisbon, Paris Saint-Germain and Chelsea respectively, momentum appears set to continue.

Liverpool's industry brought further disruption to United who, with Ryan Giggs a surprise inclusion on the right wing, oddly lacked composure. The game opened at a breathless pace and remained at a high intensity, with challenges and temperatures to match. Patrice Evra and Ashley Young immediately took the game to Liverpool but it was the home side who dealt the telling early blow with a goal that epitomised their work-rate and intelligence.

Jordan Henderson pressed Young into submission near the United penalty area. The ball broke for Sturridge and, though Rio Ferdinand read the striker's shot to deflect wide, he was not so alert at the resulting corner. Agger twisted and turned to steal a yard on Ferdinand and headed Steven Gerrard's corner goalwards. Sturridge, showing supreme awareness, stepped forward off the goalline to back-flick a header between Evra and Tom Cleverley. Anfield erupted and the England international sprinted into an embrace with Rodgers in celebration of his fifth goal in four matches this season.

Van Persie almost equalised immediately with an overhead kick from Evra's header but sent the effort skywards. It was to be the start of a frustrating, fortunate afternoon for the Dutchman, who was unable to convert Young's corner when it flashed across the face of the Liverpool goal shortly afterwards. Welbeck, frequently on the end of a verbal bashing from Giggs, also missed a fine chance when he stepped inside Skrtel and took a split-second too long to let fly, allowing Glen Johnson to block. The ball struck the right-back's arm but there were no appeals from United.

The visitors were patient in possession but, with Philippe Coutinho, Iago Aspas and Henderson dropping back into a compact Liverpool midfield, they rarely sensed a route through. Giggs and Van Persie were the worst offenders with a loose final ball when opportunities did arrive and discipline was also a problem following Phil Jones's exit with an ankle injury.

Cleverley scythed down Coutinho as Liverpool refused to stop play with Jones writhing in agony. That responsibility belongs only to the referee and Andre Mariner deservedly showed the United midfielder the first yellow card of the day. He then booked Van Persie for a cynical foul on Agger. In the same passage of play the United forward had dived over Lucas's challenge. Not content with testing Mariner's patience, Van Persie raised an arm to Skrtel in first-half stoppage time for an alleged elbow by the Slovakian. United's focal point could have been dismissed by a stricter referee, a point no doubt raised by Gerrard and as he and Nemanja Vidic held a lengthy captains's conference with Mariner at half-time.

Valencia's introduction for Jones, and a shift from 4-4-2 to 4-2-3-1, injected much-needed urgency to the United attack and the visitors carried the greater threat in the second half, without forcing Simon Mignolet into one demanding save until the 78th minute. Welbeck was rightly refused a penalty when he tumbled under an innocuous Aspas touch and Valencia finally stretched the Liverpool keeper with a powerful drive from the edge of the area.

With three minutes remaining, Hernández played Van Persie into space behind the Liverpool defence. Anfield held its breath, United sensed a reprieve and the striker hit the advertising hoardings. The champions must now find the target on transfer deadline day.

Man of the match Martin Skrtel (Liverpool)