An action-packed second half overshadowed what happened before the break – Manchester United started brilliantly, and thoroughly outplayed Liverpool.

Brendan Rodgers’ switch to this 3-4-3 formation for the 3-0 defeat at Old Trafford in December proved the turning point in Liverpool’s campaign, but this was the second time this week that Liverpool struggled to impose themselves, following a poor display at Swansea. Again, they were overrun in midfield.

One of the star performers was Michael Carrick, who sat deep in midfield unchallenged by Liverpool players and helped to put United in control with quick, sharp passing. He also played intelligently without the ball – often sticking tight to Philippe Coutinho or Adam Lallana, but refusing to be dragged out of his natural position. He made timely interceptions and covered diligently whenever one of the centre-backs moved forward to track an opponent, showing exactly why Louis van Gaal awarded him a one-year contract extension this week.

Carrick was not entirely faultless – in fact, he was partly responsible for Manchester United’s concession in the second half. But considering the struggles of other holding midfielders against this Liverpool system – Mathieu Flamini’s display in a 2-2 draw at Anfield shortly before Christmas springs to mind – this was an important display in a difficult role.

The other interesting area was out wide. A three-man defence often appears more like a back five in a defensive approach. This, however, was a bolder strategy from Rodgers. He instructed Raheem Sterling and Alberto Moreno, two very quick, attack‑minded wing-backs, to push forward onto Daley Blind and Antonio Valencia whenever possible, leaving Coutinho and Lallana infield, and passing on responsibility for the opposition wingers to Liverpool’s centre-backs. This means players must make difficult decisions, however, and sometimes Liverpool got it wrong.

The obvious example was the opening goal, scored by Juan Mata after a fine passing move in an excellent spell of possession for the away side. Moreno was caught too high up the pitch, anticipating a crossfield ball to Valencia, and found his compatriot Mata charging in behind him. Moreno’s positioning was poor – and he was caught out later for Mata’s superb acrobatic second too – but part of Rodgers’ game plan was for the wingers to press high.

Alberto Moreno was caught out for Manchester United’s opener, anticipating a ball to Antonio Valencia and letting Juan Mata run past him to score. Photograph: Michael Cox

United’s buildup followed a similar pattern to last weekend’s 3-0 win over Tottenham Hotspur. It was generally short and high-tempo, although when Liverpool pressed high up the pitch United were happy to bypass the midfield with long balls to Marouane Fellaini in the inside-left channel. He won his first header within the opening 10 seconds, although did not dominate as he had against Tottenham the previous weekend. Attempts to feed Wayne Rooney were generally unsuccessful, and the striker’s touch was poor when dropping into deep positions – United’s slick passing moves rarely involved their captain.

Rodgers had reshaped effectively at half-time against Swansea, and changes were inevitable this time around too. Steven Gerrard was introduced in place of Adam Lallana, probably for his leadership qualities as much as for tactical reasons, but his dismissal came so quickly that it was difficult to ascertain how Rodgers had changed things.

A frantic second reorganisation was therefore necessary and Liverpool coped reasonably well with 10 men in a rough 4-3-1-1 system featuring Sterling behind Daniel Sturridge. Even when Mata doubled United’s lead, Rodgers was determined to turn the game around, and his second substitution was an extremely attacking move at 2-0 down, bringing on Mario Balotelli for the struggling Moreno and playing him alongside Sturridge with Coutinho just behind.

Liverpool ended up with Raheem Sterling and Emre Can pushing forward aggressively from full-back, helping to contribute in midfield. In fact, Liverpool were probably better with 10 men than 11, which only demonstrates how they had been thoroughly outplayed in the first half.