The Egyptian's sole goal half way in to the first half was enough for Jurgen Klopp's side to keep pace with Pep Guardiola's first-placed Manchester City.
The Reds saw out the fixture despite the home side proving to be a tricky side and David Wagner's side had their fair share of chances.
The Reds looked sharp early on with Sturridge impressing in Roberto Firmino's usual false nine role. However, chances didn't come too easily for the visitors.
Salah and Sturridge then soon swapped positions, with the Egyptian looking to threaten The Terrier's centre-back pairing with runs in behind.
It paid dividends moments later when Joe Gomez’s slotted a pass in to Shaqiri, who turned intelligently and delivered a reverse pass into Salah, who made no mistake in his classy finish.
The number 11 clipped the ball low across goalkeeper Jonas Lossl, hitting the far post and going in to put the Reds ahead.
Whilst the Reds were dominant in the early stages, Huddersfield managed to play themselves in to the game as the first-half wore on, and the Reds were lucky to hold on at times.
Klopp's side were given a let off when Jonathan Hogg took aim from 20 yards with a sweetly struck half-volley that crashed against Alisson's right-hand post to fly clear.
Philip Billing then curled a free-kick wide of Alisson Becker’s goal, and moments later there were appeals for a James Milner handball and penalty, only for Michael Oliver to waive them down.
Alex Pritchard then put Norwich ahead as the ball fell to him from close-range, however the strike was disallowed for offside by the fourth official.
Huddersfield had the first real attempt in the second half when Laurent Depoitre's header was comfortably taken by Alisson who dove to his left.
Fabinho replaced a cramping Lallana to make his first Premier League appearance 20 minutes from time, whilst Shaqiri moved further forward. Roberto Firmino was later introduced for James Milner and slotted into the Reds' midfield.
However, the Beninese skewed his shot over the crossbar from close-range as the Reds held on to three points.
Next up for Liverpool is Red Star Belgrade in the Champions League group stage at Anfield, whilst they face Cardiff at home in the Premier League at the weekend.
Huddersfield Town: Lossl; Zanka, Schindler, Lowe; Hadergjonaj (Mbenza 69′), Mooy, Hogg (Diakhaby 90′), Billing (Mounie 69′), Durm; Pritchard; Depoitre.
Liverpool: Alisson; Gomez, Lovren, Van Dijk, Robertson; Henderson (Wijnaldum 45′), Milner (Firmino 76′); Salah, Shaqiri, Lallana (Fabinho 69′); Sturridge.
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