Adam Higson and Jamie Acton tries got Leigh on the way in the first half, both converted by Ben Reynolds.
Harrison Hansen, Reynolds and Sam Hopkins all went over after the break, while continuing to hold out the Giants attack with some solid goal-line work.
Defeat means Giants have conceded 78 points in losing back-to-back games.
Promotion to Super League last season ended a 12-year absence from the top tier, and the class of 2017 have already matched the 2005 side's two wins for the season from just five matches.
Huddersfield were bolstered by the return of key players such as England winger Jermaine McGillvary, centre-partner Leroy Cudjoe, and back-rower Ukuma Ta'ai but they found Neil Jukes' side an impenetrable barrier.
Leigh, by contrast, were clinical at times, and in Josh Drinkwater, Reynolds and hookers Micky Higham and Eloi Pelissier had the guile around the ruck to punish the visitors.
Leigh head coach Neil Jukes told BBC Radio Manchester: "Defensively we were really good all night, tenacious in what we've done but ball in hand we kill ourselves. When we put 12 sets together at the end we posted a lot of points and pressure.
"The place is rocking and we're climbing up the table. The players worked really hard, but we can't win a game with what we tossed up last week with the ball in hand. Today we put good stints together and challenged them.
"We've just got to get more consistent with our attack."
Huddersfield Giants head coach Rick Stone told BBC Radio Leeds: "We knew it would be a tough contest and it was for the majority of the game but we lacked a lot of execution.
"It hasn't been an issue for us this season but I'm disappointed in the result and how it panned out. We didn't have too many imaginative players out there tonight.
"Full credit to Leigh their defensive game was good, we had plenty of chances to score some points but couldn't score them."
Leigh Centurions: Hampshire; Higson, Brown, Crooks, Dawson; Reynolds, Drinkwater; Tickle, Higham, Acton, Vea, Hock, Hansen.
Replacements: Pelissier, Burr, Hopkins, Green.
Huddersfield: Gaskell; McGillvary, Cudjoe, Mellor, Murphy; Brough, Brierley, Rapira, Leeming, Ikahihifo, Roberts, Ta'ai, Hinchcliffe.
Replacements: Wakeman, Clough, Smith, McIntosh.
Referee: Chris Campbell (RFL).
Leigh Centurions notched their second Super League win this season, hammering an off-colour Huddersfield Giants without conceding a single point.