An own goal by Jakub Kiwior and a thumping late strike by Luis Diaz sealed a 2-0 victory for Liverpool at Arsenal in the weekend's headline FA Cup third round tie as the hosts' dismal form extended into the New Year on Sunday.

Arsenal wasted a sackful of chances in the first half and were made to pay as Liverpool skipper Trent Alexander-Arnold's free kick glanced off the head of Kiwior in the 80th minute.

Diaz then made sure of eight-time winners Liverpool's place in the fourth round draw as he lashed home in stoppage time.

Premier League leaders Liverpool had been second-best in the opening period with Arsenal unable to make the most of a flurry of early chances -- captain Martin Odegaard coming closest as he rattled the crossbar with a powerful drive.

Liverpool improved after the break though and their 7,000 army of travelling fans were rewarded with a two late goals.

Arsenal have now lost their last three games in all competitions.

"We changed things around at halftime internally, and we came out and played football and created chances," Alexander-Arnold said.

"There were times in the first half that we were a little bit naive ... We hit the woodwork a couple of times, so we've had our chances, and towards the end, we put them away. "