Prior to the defeat to United, Liverpool had gone five straight league games without a loss ( four wins, one draw), while it was United’s third straight league win.
United’s record signing Paul Pogba was replaced by Juan Mata due to injury which he sustained in training on Friday.
The early part of the game was edged by Liverpool but without any clearcut chances.
But it was United who broke the deadlock in the 14th minute thanks to Rashford who cut in to his right foot before rifling his effort into the far corner.
Four minutes later Liverpool went close only for Roberto Firmino’s cross to evade Sadio Mane at the far post.
United doubled their lead in the 24th minute, once again through Rashford who swept the ball past Loris Karius after Liverpool failed to clear their lines.
United went close in the 38th minute off a brilliant acrobatic effort by Juan Mata which went narrowly wide.
With two minutes left in the first half, Andrew Robertson sent in a dangerous low cross but Ashley Young did well to clear the danger.
Three minutes into the second half, Virgil Van Dijk went close for Liverpool but his header at the back post went over the bar.
Liverpool, who dominated in terms of possession, continued to search for their first goal with James Milner attempting a long range strike which failed to bother De Gea.
In the 66th minute Liverpool pulled a goal back as Bailly turned Mane’s cross into his own net.
With four minutes remaining in the game, Dejan Lovren denied Mata with a huge interception to keep the scoreline at 2-1.
Liverpool poured forward for the equaliser and were almost rewarded only for Georgino Wynaldum’s effort to be blocked away for a corner.
Six minutes were added and Mohamed Salah had a chance to draw Liverpool level only to volley his effort over the bar.