Aidan Sezer kicked a late penalty to make it two wins out of two for Huddersfield - their best start to a Super League season for six years.
Adam O'Brien's try put them in front before Ken Sio responded for Salford.
In a tight second half, Dan Sarginson's score put Salford ahead but teenager Louis Senior's try levelled the match at 10-10.
After Sezer's all-important kick on 78 minutes, Sio almost crossed for Salford but was crowded out.
Salford, who made the Grand Final last season, have now lost two of their opening three league games.
With the hosts having lost James Greenwood, who went off after a heavy collision and failed a subsequent head injury assessment, Huddersfield opened the scoring when hooker O'Brien darted under the posts.
Sio replied for Salford after being sent over in the corner by Niall Evalds.
Dan Sarginson put Salford ahead with a try early in the second half It was a case of third time lucky for Sio, who had been denied tries by superb last-ditch tackles from Sezer and 19-year-old Senior.
Sio's try was a much needed boost for Salford before the interval and they went ahead eight minutes into the second half when Sarginson went through after being found by Kevin Brown.
However, Huddersfield quickly levelled when Sezer supplied Senior on the left wing and the youngster registered his second try for the Giants.
Salford ended the match a man short after Brown was sin-binned following a confrontation with Jordan Turner with six minutes remaining.
And when Lee Mossop was penalised for offside, the reliable Sezer capitalised.
Salford head coach Ian Watson:
"The players (Brown and Turner) were both tangled up and you want them to just get up and play the ball. We've had a situation where the referee has decided the game.
"If the cameras weren't here certain decisions wouldn't have been made. It is about fine margins and maybe having cameras at every game is the right way to go.
"I thought it was a great game - a real good arm-wrestle. There are areas we can improve on and we are going in the right direction."
Huddersfield head coach Simon Woolford:
"We would have lost that game 100 times out of 100 last season but the harder you work the luckier you become.
"I thought a couple of decisions late in the game went our way but our attitude towards defending our line was there for all to see. The most important thing for me is that we found a way to win.
"You don't win competitions in February but you can certainly lose them - we saw that last year when we won just one of our last six and our season was dead and buried.
"We have recruited really well and have a healthy squad so that helps."
Leeds Rhinos (6) 22 Tries: Gale, L Briscoe, Oledzki, Walker Goals: Gale 3
Leeds Rhinos came from behind to record their second win of the Super League season, beating last year's losing Grand Finalists Salford Red Devils.
Niall Evalds scorched in and Tui Lolohea muscled his way over down the same right edge to put Salford in front, with Luke Gale replying.
Leeds went in front for the first time when Luke Briscoe touched down, and Mikolaj Oledzki went in shortly after.
A Gale penalty and Jack Walker's breakaway score sealed Leeds' victory.
Ian Watson's Salford were in some respects the story of 2019 but having lost the influential Man of Steel Jackson Hastings to Wigan and Great Britain team-mate Josh Jones to Hull, they have not been able to kick off the campaign in the rip roaring way they ended the last.
Leeds were well beaten in their opening match by Hull FC but morale-boosting wins over Hull KR and now the Red Devils suggest their new arrivals such as Gale and Matt Prior have acclimatised to the system.
On a chilly afternoon with the wind swirling at times, Leeds showed mettle to fight back against a home side who initially adapted better to the conditions.
They took advantage of field position and a penalty for a high shot on Chris Atkin to score down the right through Evalds, and Lolohea targeted the same defensive unit to charge over against his old club.
However, the loss of Krisnan Inu to a knee injury and Luke Yates after he failed a head injury assessment, plus missed goal kicks, gave Leeds hope and they got themselves on the board when a sparkling break by Rhinos hooker Brad Dwyer from dummy-half just before the break was finished off by the supporting Gale.
Salford had opportunities in the second period, with Joey Lussick twice held out, but Leeds ended up taking their chances to run out clear winners.
Leeds forced a drop out and made the most of the opportunity when the ball went right and Briscoe dived in spectacularly.
Oledzki then hit a short ball to crash over as Leeds struck again and after Salford coughed up possession in a promising position, the visitors broke 80 metres with Walker finishing off in the corner.