The Reds' title credentials will be tested while their star man is away with Egypt at the Africa Cup of Nations. But Jota and Nunez stood up to be counted to secure a vital win at one of the form sides in the Premier League.
Bournemouth had lost just once in their previous nine games to climb comfortably clear of the relegation zone. However, the Cherries were held at arm's length in the first half before Jurgen Klopp's men turned on the style after the break.
The visitors were restricted to pot shots in a first period devoid of clear chances. Alexis Mac Allister and Nunez tested Neto from long range. But the game turned on one moment of quality from Liverpool to break the deadlock on 49 minutes.
Jota's first time pass put Nunez in the clear and the Uruguayan showed the poise he has often lacked in his Liverpool career to date to slot into the far corner. Substitute Cody Gakpo then teed up Jota to fire in at the near post 20 minutes from time to end the game as a contest.