Going into the match needing a win to secure qualification for the Europa League’s last 32 ahead of Switzerland’s Young Boys, the midfielder struck the vital winner midway through the first half.
The decisive nature of the match meant that Liverpool boss Brendan Rodgers selected a fairly strong lineup featuring talisman Luis Suarez as well as the likes of Joe Allen, Glen Johnson and Martin Skrtel.
It was a somewhat subdued atmosphere inside the Stadio Friuli with the home side already eliminated and boss Francesco Guidolin having responded by leaving out the influential Antonio Di Natale.
It was Liverpool who gained control of the match early with their short passing game, although the visitors’ midfield had to be disrupted in just the 12th minute as a facial injury to Nuri Sahin meant the on-loan Real Madrid man being replaced by Jonjo Shelvey.
Udinese managed a couple of early efforts on goal as first striker Mathias Ranegia headed wide from 12 yards and then Roberto Pereyra’s inventive curling lob from the angle was tipped over by Pepe Reina.
But there could be little complaints when Liverpool took the lead in the 23rd minute. Suarez got his head to a corner and the ball reached Suso near the byline, who displayed awareness to pull it back to Henderson and the former Sunderland man struck first-time past Daniele Padelli.
Just a few minutes later, Liverpool had the ball in the net once more through Johnson, but the strike was correctly ruled out as Stewart Downing was offside when playing the ball across the box.
Suarez, who will be suspended for Liverpool’s trip to West Ham on Sunday, was looking to make the most of only his second Europa League start of the campaign. On the stroke of half time, the Uruguayan performed a fine overhead kick that Padelli had to tip over the bar to keep the score at 1-0 heading into the break.
Liverpool had a golden opportunity to make their path to the knockout stages a more comfortable one just two minutes after the restart. Suarez did brilliantly to create an opportunity for Suso with a fine run and pass, but the young Spaniard put his shot wide of the near post.
Rodgers’ side were to be left frustrated midway through the second half by two fine saves from Padelli. The Italian perhaps having particular incentive to perform, having played just a single game for Liverpool during a short loan spell back in 2007.
First Henderson met a left-wing Jose Enrique cross with a crisp and controlled volley on his instep, but the ball traveled just too close to Padelli, who was able to display some fine reflexes to tip over the bar.
Minutes later Suarez displayed his trickery in the box as he received a ball from Downing down the right of the area and turned inside one defender before doing likewise to a second and then prodding a left-footed effort at goal from close range that required Padelli to make a stunning stop to parry the ball behind.
Just as Liverpool were perhaps starting to feel the tension of a slender lead heading into the final stages, Udinese looked to have eased the visitors’ task when Giovanni Pasquale was shown his second yellow card for a late clumsy challenge from behind on substitute Raheem Sterling.
With Young Boys comfortably defeating Anzhi, it would still have taken just one goal to change the whole complexion of the group.
And there was to be an incredible finish to the match as Di Natale, on for the final stages, almost sent Liverpool crashing out but fired over the bar from eight yards after a one-two with Davide Faraoni.
Liverpool were left breathing a heavy sigh of relief and at the final whistle, with the tightness of the section summed up by the fact that Liverpool ended up topping the group as they await the draw for the next round in two weeks’ time.