The west Yorkshire side slipped to a seventh successive defeat, although captain Chris Thorman had a late chance to snatch a draw when he pulled a penalty wide.
Salford claimed only their second win of the season after holding their nerve to edge a tense encounter at the Galpharm Stadium, where they suffered three emphatic defeats in 2006.
Another narrow defeat was tough on Huddersfield, who dominated the match for long periods and have the third best defence in the league but badly lacked creativity in attack.
Despite enjoying an overwhelming share of possession, the Giants trailed 12-4 after conceding a brace of Luke Robinson tries which came against the run of play.
The scores illustrated Huddersfield