Marcus Rashford put the hosts ahead in controversial circumstances in the 36th minute after they broke away on a counter.
Liverpool felt like they should have had a free-kick after Divock Origi went down under a challenge from Victor Lindelof.
However, play went on, with Daniel James delivering a brilliant cross for Rashford to tuck home.
VAR carried out a check for a foul but the goal stood nonetheless.
The visitors dominated possession for the larger parts of the second-half, and finally equalised in the 85th minute through Adam Lallana.
The midfielder tucked away an inch-perfect cross from Andrew Robertson to score his first goal in more than two years.
While the Scotland international turned provider this time out, his teammate and fellow full-back Trent Alexander-Arnold also impressed.
The performance of the youngster caught the attention of Match of the Day presenter Gary Lineker, and he reacted thus on Twitter:
The passing range of @trentaa98 is extraordinary. 👌🏻
— Gary Lineker (@GaryLineker) October 20, 2019
Alexander-Arnold created a couple of chances for Liverpool, and will look to play another huge role this term after going into the record books for his input last term.
The 21-year-old became the first defender to register most assists (12) in a single Premier League campaign and has already assisted two goals this term, scoring once.