Livingston made 10-man Motherwell pay a heavy price as second-half goals from Bruce Anderson and Sean Kelly earned them a first home league win of the season.
With the match goalless in trying weather conditions, the visitors had youngster Lennon Miller sent off in first-half stoppage time.
Livi made the most of their man advantage after the break as they grabbed all three points.
Anderson flashed in the opener in the 53rd minute and Kelly’s penalty nine minutes later sealed victory.
In a lively opening, both sides forced corners inside the first two minutes. From the second, Livi defender Ayo Obileye glanced his header across goal and wide from Sean Kelly’s delivery from the left.
That opportunity encouraged the home side and they enjoyed the better of the opening exchanges before almost getting the breakthrough they sought in the eighth minute.
Joel Nouble threaded a pass wide for Dan MacKay and the on-loan Hibernian winger brilliantly picked out the run of Stephen Kelly with his cutback.
However, twice the midfielder saw efforts at goal blocked by the retreating Motherwell rearguard.
It was a day for defensive bravery and at the other end Sean Kelly was resolute as he got his foot in the way of a Theo Bair shot on the break.
It looked like the kind of game that was going to take something special to find a breakthrough, and it almost came in the 30th minute.
Motherwell were awarded a free-kick on the halfway line and, spotting Shamal George off his line, defender Dan Casey attempted an outrageous effort on goal that the Livi keeper scrambled back to tip over his crossbar.
In first-half injury time, the Fir Park men were reduced to 10 men in the game’s decisive moment.
Anderson held the ball and fed the supporting MacKay, whose run took him beyond the ‘Well defence, only for the covering Miller to clip his heels and send the wing-back sprawling.
The VAR check confirmed Don Robertson’s decision to red card the youngster, but Sean Kelly could not take advantage as he sent the free-kick straight into the arms of brother Liam in the visitors’ goal.
It took just seven minutes of the second half for Livi to find the opener though.
Faced with defender Brodie Spencer, MacKay left him for dead and flashed in a low cross from the right that Anderson flicked in at the far post from just inside the six-yard box.
The home side rammed home their advantage as they doubled their lead in the 62nd minute.
An attack down the left was halted when James Penrice was caught late by Bevis Mugabi just inside the box and whistler Robertson pointed to the spot.
Sean Kelly got the better of sibling Liam in the ‘Well goal as he sent him the wrong way to find the net.
Livi thought they had a second spot-kick with 15 minutes remaining when Jason Holt’s heels were clipped by substitute Georgie Gent.
But a VAR check indicated the offence could had taken place outside the box and Sean Kelly could not make anything of the free-kick wide on the right as the home side saw out time comfortably.
Trophies still the target for Ten Hag despite Liverpool setback
Erik ten Hag insists Manchester United will push for trophies this season despite a humiliating 3-0 defeat to rivals Liverpool at Old Trafford on Sunday.
Ten Hag, who won the EFL Cup and FA Cup in his first two terms with the club, watched on as Luis Diaz's double and Mohamed Salah's second-half strike secured an impressive victory for the visitors.
While the statistics suggest it was a closely contested affair, Liverpool punished a series of errors from United at a disgruntled Old Trafford, with Casemiro and Kobbie Mainoo both culpable for senseless turnovers.
Of the Red Devils' eight shots, meanwhile, only three threatened Alisson's goal, as they ended the contest with an expected goals (xG) total of 1.36 to Liverpool's 1.73.
But despite an underwhelming display ahead of the international break, Ten Hag is confident he can add more silverware to United's trophy cabinet this campaign.
"You can see the xG, we didn't concede as many goals. I don't think we are in the same pattern. It was sometimes open and we took risks," he told Sky Sports.
"But I don't want to talk about this after a 3-0 defeat to Liverpool. Well done Liverpool. We have to be humble and take it.
"There are many games to play and I know where we will be at the end of the season. We will go for trophies. That will stand."
It proved to be another difficult outing for Casemiro, who gifted Liverpool their opening goal with a poor pass out from the back before being bundled off the ball in the build-up to their second.
The Brazilian completed 27 of his 37 attempted passes, losing possession 13 times, with only Noussair Mazraoui and Diogo Dalot doing so on more occasions (both 16).
Casemiro was replaced at half-time by 20-year-old Toby Collyer, with Ten Hag later saying the decision was taken for the good of the team.
"It is what the team needed. You know when you are 2-0 down against Liverpool you have to take more risks, it will be open," he said.
"When you are losing you have to take more risks. I have to give compliments to the team. You have to keep fighting and sticking together.
"You know the game and he knows the game. He will go on and we will go on. He's a great player. We will continue this season to improve the team and the players.
"Is he still able to play at the highest level? He improved and has shown so often that he is a great character.
"We all have seen great moments from him and him being decisive in midfield. He will show that again and will bounce back."
Salah eager to enjoy 'last year' with Liverpool after latest Old Trafford goal
Mohamed Salah says he "wants to enjoy" what could be his final year at Liverpool, after playing a key role in the Reds' 3-0 victory over Manchester United.
Salah assisted the opener for Luis Diaz before scoring the second - and what was his 10th goal in his last seven appearances at Old Trafford - as Arne Slot's side made it three wins from three in the Premier League.
The Egyptian became the first player to score in five successive away appearances against United in the Premier League, though his future at Anfield is uncertain.
Now into the final year of his existing contract, Salah wants to embrace every moment of his eighth season with Liverpool.
"A great result. Everyone knows the derby is important for the fans and the city," he told Sky Sports. "We need to carry on and, if you want to fight for the league, you have to win each game.
"The manager likes us to press high and there were a couple of mistakes, and we managed to punish them - it was part of the plan.
"I had a good summer, a long time to stay with myself and think positively a bit. This is my last year with the club and I want to enjoy it.
"I feel I am free to play football. We will see what happens next year. Nobody in the club has talked to me about contracts. It is not up to me, it is up to the club."
Meanwhile, Slot saluted his players as he became just the third manager to win each of his first three Premier League games without conceding, after the late Sven-Goran Eriksson (2007) and Jose Mourinho (2004).
"The first few minutes, United started aggressive, and we had to fight our way through the period.
"If you go to Old Trafford, we know there will be tough moments. After scoring a great goal [through Trent Alexander-Arnold], which was disallowed, we kept on playing as we were before.
"Today, we showed a lot of moments where the forwards tracked back so aggressively, and that is what we need if you want to win these games. It's a good win."
Manchester United 0-3 Liverpool: Salah haunts Old Trafford once again
Arne Slot maintained his perfect start as Liverpool head coach as the Reds ran riot in a resounding 3-0 victory over rivals Manchester United at Old Trafford.
Luis Diaz’s header handed the visitors the advantage 10 minutes before half-time, after Trent Alexander-Arnold had seen a potential early opener chalked off following a VAR review.
Diaz then doubled his tally seven minutes later with a low finish into the bottom corner after being picked out by an intricate pass from Mohamed Salah.
The Egyptian scored against United in the Premier League for the 12th time after the break, Liverpool punishing yet another mistake from the Red Devils' midfield to add some gloss to the scoreline.
The triumph sees Liverpool join Manchester City as the only two sides with perfect records after three matches, while United enter the international break in 14th with three points.
Data Debrief: Slot machine pays out its biggest jackpot
Liverpool's triumph marked a statement victory in Slot's early tenure, with the Dutchman becoming the second Reds boss to win their first meeting away from home against United since George Kay in November 1936.
Slot also became just the third manager to win each of his first three Premier League games without conceding, after Sven-Göran Eriksson in 2007 and José Mourinho in 2004.
But the day belonged to Liverpool's Egyptian King. Salah is the first player to score in five straight away appearances against the Red Devils in the Premier League; Dion Dublin (v Tottenham), Alan Shearer (v Leeds United), Ruud van Nistelrooy (v Newcastle), Robert Pires (v Tottenham) and Jamie Vardy (v West Brom) are the only other players to net in as many consecutive away trips to the same opponent in the competition.
Salah has now scored 10 goals in nine appearances at Old Trafford for Liverpool in all competitions. He is only the second player to score 10+ goals at a single away ground for Premier League clubs since 1992-93, after Alan Shearer (10 at Elland Road).
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