Philippe Coutinho's wonderful solo goal at the end of the first half ended this tie and ensured that the reds go into the Quarter Final draw.
Liverpool knocked Man United out of European competition in the first meeting between the two sides in continental football.
United started brightly, and were awarded a penalty that Martial scored - but they eventually ran out of steam and Coutinho sold David De Gea in the final minutes of the first half.
Second half and Liverpool dominated - they had some chances to get that second goal but with United needing 3 second half goals there was no need for the reds to gamble.
With ten minutes left the United fans started to empty the ground whilst Liverpool's travelling support continued to give their all.
James Milner returned to the side after being out with a virus last week. Alberto Moreno was the man replaced - after he had suffered a minor knock during training the previous night. Milner was chosen ahead of Brad Smith at left back - a decision that Klopp said was based on match experience.
United were on the front foot - with Liverpool looking a bit unsure early on. United's quality however was still not there - Mignolet was required to make a good save from a Lingard header, but Juan Mata should have done better with a shot that went wide.
Clyne, who has had a solid season for Liverpool, had one of his poorer days in the red shirt and he brought down Martial for the penalty that gave United some hope.
Sturridge was misfiring once again - Henderson missed a simple chance and Coutinho was snatching at chances. But a wonderful solo run from the Brazilian saw him sell a dummy to De Gea and flick past the Spaniard at the near post.
The reds equaliser on the night came just before half time. And it killed the game. It left United requiring 3 second half goals, and they never even looked like getting one from open play.
As the final whistle approached Liverpool fans were jubilant, while United fans were probably on the trains and coaches home - probably still singing their vile songs.
An important step forward for Klopp's Liverpool who must now refocus on the Premier League.
