Brendan Rodgers named a strong side, which included Luis Suarez, who is suspended for Sunday's Premier League trip to West Ham United, in the knowledge a victory would guarantee progression.
And the Liverpool boss's selection paid off at Stadio Friuli as Jordan Henderson's first-half goal proved enough to secure top spot in Group A and a place in the Europa League's last 32.
It was a slow-paced opening 20 minutes and Liverpool suffered a setback before the quarter-hour mark when Nuri Sahin had to be replaced by Jonjo Shelvey due to a nose injury.
But Liverpool then got their goal in the 23rd minute as former Sunderland man Henderson opened his account for the season.
The £16million summer 2011 signing finished a nice move from a corner after being set up by Suso, who had been found by Suarez's header.
Rodgers' team's lead could have increased on the stroke of half-time but Suarez was denied by a wonderful reflex save by Udinese's former Liverpool goalkeeper, Daniele Padelli.
Udinese posed more of a threat after the break but Liverpool, with Suarez in typically livewire form in attack, always looked a danger on breaks forward.
The visitors were given a warning in the 60th minute, when zonal marking at a corner was almost exposed as Mathias Ranegie headed over the crossbar.
And with Young Boys then winning against Anzhi Makhachkala in Group A's other game, Liverpool were on the knife edge of knowing they would be eliminated if they conceded.
But Udinese's hopes of an equaliser were crushed in the 80th minute when Giovanni Pasquale was shown a second yellow card and even star striker Antonio Di Natale's 85th-minute introduction could not save the day.