Through the first two rounds of Premier League fixtures, there had been no case for Manchester United's defence. At Old Trafford on Monday, Liverpool's went completely missing.

A week is a long time in football, to use the most fatigued of tired cliches. United had just over a week to stew over their 4-0 humbling at Brentford, during which there was no shortage of talk about another prospective hammering from Jurgen Klopp's consistently merciless Reds. 

Yet after United pressed and harried their way to a surprise 2-1 win in front of a raucous home crowd whipped up by the latest round of protests against the Glazer family's ownership of the club, it will surely be Liverpool who have to face headlines pointing to a crisis among a group of players who have set such remarkable standards in the recent years of Klopp's tenure.

It would be an exaggeration to label Liverpool as a team in crisis – they were without nine first-team players for this derby – but, as the persistent squabbles between Virgil van Dijk and James Milner illustrated, there are certainly problems to fix at the back.

Though the focus may have been on their public disagreements, the first of which came after Jadon Sancho produced composure that has been largely lacking since his move from Borussia Dortmund to put United 1-0 up in the 16th minute, in the aftermath of this game there is more likely to be scrutiny on the performance of the defender to Van Dijk's right.

While Van Dijk was partly at fault for the opener after failing to close down Sancho, it was a goal that was a direct consequence of the frequent success United enjoyed when attacking Trent Alexander-Arnold.

To blame in part for the first goal, Alexander-Arnold was tormented by Anthony Elanga in the first half and had a similarly torrid time when Marcus Rashford switched to the left flank for the second. It was Rashford who doubled United's lead, ending a run of 997 minutes without a goal in all competitions for United by coolly finishing after a counter-attack with Alexander-Arnold conspicuous by his absence.

Alexander-Arnold, regularly maligned for his defensive deficiencies, conceded two fouls and lost possession a game-high 24 times in a performance to swiftly banish from the memory.

Yet to point the finger squarely at him would be to ignore the struggles of those in front of him. Milner, who won under half of his 16 duels, and Jordan Henderson offered little in the way of control or protection for the Liverpool backline. Both were eventually withdrawn in the second half, injury robbing Klopp of the opportunity to introduce a clearly desperately needed Thiago Alcantara.

To focus on Alexander-Arnold and Liverpool's failings would also do a disservice to the impressive nature of United's display.

Scott McTominay, with Casemiro, his new team-mate in the engine room, watching on, was sublime in midfield, his 10th-minute throughball for Bruno Fernandes deserving of a goal that the right-hand post denied Elanga.

Fernandes, forlorn in the two opening defeats, had nine final-third entries, more than any other United player. Rashford, meanwhile, was a player rejuvenated, recording five of United's 12 shots.

At the back, Lisandro Martinez brushed off jokes and questions about his diminutive stature to deliver an all-action showing that featured three blocks, including one clearance off the line to prevent a Fernandes own goal, while left-back Tyrell Malacia's five tackles were the most of any player.

For all the standout displays, United could not stop Mohamed Salah from fraying the nerves with a header after David de Gea denied Fabio Carvalho.

Yet the fact United did not allow that setback to spark a collapse is testament to the speedy turnaround Erik ten Hag – who became the first Red Devils boss to secure his maiden competitive win against Liverpool – engineered in the wake of their meek surrender at Brentford.

Klopp will almost certainly dismiss any crisis talk about a team who suffered their first defeat in 22 Premier League games and have failed to win their first three Premier League games for the first time since 2012-13. However, after seeing his side concede the first goal for the seventh successive league fixture and fail to recover, Klopp must find solutions that have the same impact of those Ten Hag discovered in the compelling latest chapter of this great rivalry.