They had to work hard for the draw though as James Milner opened the scoring for Jurgen Klopp's side from the penalty spot after Paul Pogba handled the ball in the area before the half hour mark.
Jose Mourinho's side had their chances throughout the game to get back on level terms, but just as it looked like it wasn't going to be their day, Zlatan Ibrahimovic headed home his 14th league goal of the season to rescue a draw for the hosts.
The result means that United stay in sixth place while Liverpool stay in third place but have lost some ground to Chelsea at the top of the table.
Visitor's dominate early without much luck
Straight from the first whistle, the visitors started well having loads of possession with some last ditch defending from the hosts preventing any early disasters.
It was intriguing to see the way that the visitors were going to set up and it was clear from the off that they were playing in a diamond formation that kept the ball well at the start.
After getting through the first 15 minutes though, United should have went in front when a brilliant through ball from Henrikh Mkhitaryan found Paul Pogba but somehow he dragged his left foot wide when it looked like he was going to score.
Milner scored from the spot to give the visitor's the lead
Pogba's disastrous first half got worse before the half hour mark when he handled the ball in the box from a corner kick and referee Michael Oliver had no doubts and pointed straight to the penalty spot.
Milner stepped up to take it for the visitors and put it into the back of the net passed the out stretched hands of David de Gea to give the visitors the crucial lead.
Hosts failed to take their chances in the first half
The goal seemed to wake up a bit and but for a superb save from Simon Mignolet from a a free kick from Ibrahimovic from the edge of the box, the scores would have been level.
The hosts created another superb chance before half time when Phil Jones played a great through ball into the path of Mkhitaryan but he also saw his shot brilliantly saved by Mignolet, who was showing his worth to his team as he saw his side in at half time with the lead.
Visitor's almost went two in front but De Gea kept United in the game
The start of the second half was similar to the first as the visitors looked comfortable as they pushed forward looking for a second goal.
They almost got it when Philippe Coutinho, on as a second half substitute, played a lovely reverse pass into the path of Georginio Wijnaldum, who was through on goal, but saw his shot well saved by De Gea.
United responded well after that chance and should have got themselves back on level terms when Mkhitaryan was through on goal but his ball across the box evaded Anthony Martial in the box, who would have had a tap in had he touched the ball.
After this though the game became very scrappy which suited the visitors as they sat deep and tried to hit United on the break.
Ibrahimovic equalised before the end to rescue a draw for the hosts
The hosts though were determined to get back on level terms and it finally came six minutes from time when Maroaune Fellaini headed Wayne Rooney's cross onto the post but the ball came back from Antonio Valencia, who crossed it back to Ibrahimovic, who headed the ball into the back of the net off the crossbar.
After the equaliser, the hosts pushed for a winner but it wasn't forthcoming as the game ended in a draw which probably was the fair result at the end of the game.