Liverpool are on 54 points, two clear of Manchester City who have a game in hand. Burnley remain second from bottom on 13 points.
City’s 2-0 win over Everton earlier on Saturday had seen Pep Guardiola’s side move one point ahead in the table, and a packed Anfield expected a blistering start from the home side looking to reclaim top spot.
Instead, the stadium record attendance for a league game of 59,896 saw Burnley pose the greatest threat early on as Liverpool struggled to find a foothold.
“I can really imagine how Vincent Kompany is feeling right now because they did a lot of good stuff and made it really uncomfortable for us,” Jurgen Klopp told Sky Sports.
Kelleher was called into action early on, coming out to block down an effort from Zeki Amdouni as Burnley created the early danger.
Liverpool began to grow into the game but had little to show for their efforts until Burnley keeper James Trafford‘s error at the corner kick.
Alexander-Arnold whipped the corner in and Trafford came out to claim it but got nowhere near the ball and Jota had an easy header to give Liverpool the lead in the 31st minute.
Burnley never gave up, and in the 45th minute O’Shea directed a powerful header from a corner beyond Kelleher into the far top corner for his first Premier League goal.
Liverpool came out with renewed energy after the break, and retook the lead within seven minutes. Harvey Elliott, a half-time substitute, played a ball across goal which took a deflection before Diaz dived in with a header from close range.
“We knew at halftime what we had to do. We were in control but of course we had to change Trent Alexander-Arnold and are short on defenders,” Klopp said.
“Curtis Jones did incredibly well, like Harvey Elliott did when he came on.”
Fofana was through again but with only the keeper to beat he pulled his curling effort just wide of the post.
“Burnley gave problems and we had to score at the right moments. We needed Kelleher as it was a really good game for him,” Klopp told the BBC.
With 11 minutes to play, Liverpool wrapped up all three points. Another corner fell to Jota but after his shot was blocked down he passed to Elliot and his floated ball found Nunez who leaned back and headed into the far bottom corner.
There was no way back for Burnley, and Liverpool could have had another in added time but Trafford saved a close range effort when Nunez should have done better.