Ten Hag made the bold decision to knock out captains Harry Maguire and Cristiano Ronaldo and was rewarded with a performance that eased the mood of crisis surrounding Manchester United and left Liverpool still searching for their first win of the season prize.
Jadon Sancho showed great control and composure to give United a well-deserved lead in the 16th minute before Marcus Rashford finished to beat Alisson with a man's pass coming on for Anthony. Martial eight minutes after the interval.
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Mo Salah put in a tense finish as he headed home in the ninth minute but United survived to give Ten Hag the kind of win he needed to make his mark at Old Trafford.
Man Utd rise to the occasion
Manchester United were at their lowest ebb after a 4-0 humiliation at Brentford followed an opening day home defeat by Brighton.
And while thousands protested against the ownership of the Glazers before kick-off and the chants continued throughout the game, United's fans rallied behind a performance of fierce intensity and commitment that left Liverpool bullied for long periods.
New £60m signing Casemiro was paraded in front of the Stretford End before kick-off and how he must have relished the magnificent atmosphere inside Old Trafford as United turned the misery of their abject first two league performances on its head.
Liverpool won 5-0 here last season and 4-0 at Anfield but United mustered more energy and aggression in the first 10 minutes here than in both of those embarrassing performances.
Ten Hag employed pace to take advantage of Liverpool's high defensive line and they should have been ahead even before Sancho opened the scoring, Anthony Elanga hitting the post after racing clear.
United contested every challenge with a fired up Lisandro Martinez setting the tone early on with a robust challenge on Mohamed Salah.
Rashford's form has been indifferent in recent times but his confidence will surely soar after the composed manner in which he scored what eventually proved to be the winner.
And this was a landmark night for Ten Hag, who knew his decision to leave out Maguire and Ronaldo would have brought scrutiny had United lost.
Instead, he enjoyed the sort of night that he will hope gets his Old Trafford reign up and running.
Mediocre Liverpool fall short
Liverpool's disappointing start to the season continued as they found themselves over-run from the kick-off by an inspired Manchester United.
Jurgen Klopp's side have injury problems and Darwin Nunez's moment of madness that resulted in a red card against Crystal Palace deprived Liverpool of the height in attack that might have exploited Martinez's lack of stature but they got exactly what they deserved here - nothing.
Klopp's decision to omit Fabinho was mystifying, even more so when James Milner and Jordan Henderson were left off the pace as United rattled into challenges and contested every ball with a fierce competitive edge.
Liverpool were also vulnerable at the back, with Virgil van Dijk's poor start to the season continuing, especially with a passive piece of defending for Sancho's goal.
Klopp will not be panicking and Liverpool have too much quality to struggle for long but two points from their first three league games is a bitterly disappointing return and it is hard to make a case that they deserved anything more.
