Mohamed Salah scored the only goal of the game midway through the first half with a clinical finish, but Liverpool were forced to withstand some heavy pressure from the hosts in order to return to winning ways after four games without a victory.
The result means that Liverpool have now made their best-ever start to a Premier League season, whereas Huddersfield remain winless and sit 19th in the table after relegation rivals Cardiff City beat Fulham earlier in the day.
Liverpool had seen Man City send out a statement with a 5-0 win over Burnley in an earlier kickoff, but they were missing the likes of Roberto Firmino, Sadio Mane and Naby Keita from their side as Jurgen Klopp made three changes.
Indeed, Salah's opener was the only shot on target in the opening 45 minutes, as he latched on to Xherdan Shaqiri's through-ball before poking the ball beyond Jonas Lossl into the far corner - a goal which ended his longest drought as a Liverpool player.
Huddersfield were unfortunate to go into the break behind, though, having begun to ramp up the pressure in the final 15 minutes of the half as Liverpool struggled to take control of the game despite their lead.
The Terriers have failed to score a single home goal all season, but they came within inches of breaking that duck shortly after the half-hour mark when Jonathan Hogg collected the ball 30 yards from goal and unleashed a rocket which crashed against the post with Alisson Becker beaten.
It was a moment which sparked the home side's improvement in the closing stages of the half, and Philip Billing also threatened from long range when his free kick flew a couple of yards wide of the target.
When Huddersfield did finally get the ball in the back of the net in front of their own fans for the first time this season they saw their celebrations cut short by the offside flag, with Alex Pritchard the man to be denied moments after Milner had survived a handball penalty appeal.
Liverpool held on to take the lead into the interval, and they almost doubled their advantage soon after the restart when Daniel Sturridge worked space for a shot, curling his effort over the crossbar from just outside the area.
Huddersfield went into the match having registered a league-low 20 shots on target this season, and it took until 10 minutes into the second half for them to register their first and only one of the game this evening when Alisson made a routine stop to deny Laurent Depoitre's header.
The visitors were struggling to offer much more, although Salah had the chance to double his personal tally shortly after the hour mark when he raced through on goal, only to this time drag his finish wide of the target.
Such openings were few and far between for Klopp's side, though, and they were almost punished for their lethargy eight minutes from time when Dejan Lovren failed to cut out a cross which fell to Steve Mounie, who sliced a golden opportunity over the crossbar from inside the area.
It proved to be the one clear chance Huddersfield had been waiting for, and it was Liverpool who created the better openings in the closing stages of the game when first Salah was thwarted by Lossl and then Firmino fired over from the edge of the box.
The Reds were able to hold on for the win despite being far from their best, though, leapfrogging Chelsea up to second place and only behind champions Man City on goal difference.
Today's results mean that three teams are unbeaten after nine games of an English top-flight season for just the third time in history, but at the other end of the table things look increasingly bleak for Huddersfield, who are enduring their longest winless run in any division since 2000.
The Terriers have also now failed to score in each of their last seven home Premier League games - the second-longest such run in the competition's history - and become only the second team after Everton in 1998-99 to fail to score in each of their opening five games of a Premier League season.
HUDDERSFIELD (3-5-1-1): Lossl; Zanka, Schindler, Lowe; Hadergjonaj (Mbenza 69'), Mooy, Hogg (Diakhaby 92'), Billing (Mounie 70'), Durm; Pritchard; Depoitre
LIVERPOOL (4-3-3): Alisson; Gomez, Lovren, Van Dijk, Robertson; Shaqiri, Henderson (Wijnaldum 46'), Milner (Firmino 77'); Salah, Sturridge, Lallana (Fabinho 69')