Salah struck the all-important goal on 23 minutes on a night when Jurgen Klopp's Reds were far from at their best, but learned the value of winning ugly in their title pursuit.
Town gave everything, but failed to find an all-important breakthrough. They have now not scored in their opening five home league matches of the season - equalling a top-flight record set by Everton in 1988-99.
They are also closing in on Manchester City's Premier League record of seven home matches without a goal, with Town's last home goal arriving back on April 14.
Town's epic wait without a goal against the Reds since April 1962 may have extended by half-time, but despite staring at an interval deficit, they was plenty to be enthused about for the hosts.
Huddersfield's response to Salah's opener was character-laden, intense and worthy of high praise, only for the luck which had not befriended Town this season - according to Wagner - to continue to be conspicuous by its absence.
Trailing to Salah's classy 23rd-minute opener, Town were desperately unfortunate not to level when Jonathan Hogg's piledriver struck the post, while the visitors survived a big penalty appeal two minutes before the break after Hogg's header struck James Milner's arm.
Soon after, the lively Alex Pritchard found the net with a dinker effort after Philip Billing's long throw was not cleared, but the 'goal' was correctly ruled out for offside against Laurent Depoitre.
It was a half in which the work ethic of Town - playing a 3-5-1-1 formation - was relentless, while they refused to be dictated by a Liverpool side who were ruffled for significant parts of the first half.
But when their moment cane to strike, they showed their clinical, when Town momentarily switched off down their left, with Joe Gomez finding Xherdan Shaqiri, whose pinpoint pass found Salah, who instantly drilled the past low past Jonas Lossl in a moment of class.
Refusing to be downheartened, Town continued to impose themselves on the restart with a patient, probing move seeing Depoitre head straight at Alisson after a hanging cross on the right from Hadergjonaj.
It was still anyone's game, even if Liverpool displayed danger on the counter, more especially at the deadly feet of Salah.
The Egyptian had a chance to seal victory four minutes after the hour mark after being sent clear, only to steer his effort wide of goal after latching onto Andrew Robertson's throughball.
Town plugged away, with Steve Mounie and Isaac Mbenza being thrown into the fray as Wagner rolled the dice.
The chance that the hosts craved arrived when the pair combined seven minutes from time - only for Mounie to wastefully fire over after a cross from his fellow substitute was not cleared.
At the other end, as gaps appeared as Town threw bodies forward, substitute Roberto Firmino blasted over an excellent chance.
Huddersfield Town: Lossl; Zanka, Schindler, Lowe; Hadergjonaj (Mbenza 70), Hogg (Diahkaby 90), Mooy, Billing (Mounie 70), Durm; Pritchard, Depoitre. Substitutes unused: Hamer, Bacuna, van La Parra, Stanković.
Liverpool: Alisson; Gomez, Lovren, Van Dijk; Robertson, Lallana (Fabinho 70), Henderson (Wijnaldum 45), Milner (Firmino 76); Salah, Sturridge, Shaqiri. Substitutes unused: Mignolet, Origi, Matip, Alexander-Arnold.
Referee: M Oliver (Northumberland)