Sadio Mane equalised with a clinical finish only for Abdoulaye Doucoure to restore the lead from close range.
Roberto Firmino's penalty made it 2-2 before Mohamed Salah thought he had won it only for Britos to equalise.
In Jurgen Klopp's 100th competitive game as Reds boss, Liverpool wasted a string of chances before Uruguay defender Britos headed over the line from close range.
Reds legend Jamie Carragher said afterwards: “It's the set up from the manager. They concede the most goals out of anyone in the top six. Nothing has changed.
“He will help but on set pieces it is not about the defence. he way Liverpool set up set piece wise, it won't make a difference.
"(Virgil) Van Dijk goes in that team it means that Lovren or Matip comes out, he won't be in that position. If he was playing today, he'd have been in their position.
“One man is not going to do that (make a difference), the position of the full-backs in general play leaves the centre-backs exposed.
“Liverpool play so high and wide that they have a centre-back exposed there all the time. One player's not going to change that."