Hooker Paul Aiton's late try, his first for Leeds, sunk Huddersfield as the Rhinos overcame their bogey side 28-24 to go top of Super League with their third win from three outings.
It was the Rhinos' first win in eight matches against the Giants, who had looked set for a fifth consecutive victory at Headingley after coming from 18-0 down to lead 24-22 with 12 minutes to go.
The Giants deserve considerable credit for a second-half fightback but they were left still looking for their first win of the season.
It looked straightforward for Leeds as Huddersfield, playing into a flurry of snow at the start, struggled to get into the game.
Second-rower Carl Ablett easily brushed off the challenge of 20-year-old fullback Jake Connor for the opening try after just five minutes and skipper Kevin Sinfield kicked the first of his four goals.
Ablett then featured twice as the Rhinos, taking full advantage of their opponents' indiscipline, ran in two further tries in a four-minute spell midway through the first half to take control.
Australian prop Adam Cuthbertson took Sinfield's short pass and bundled defender Brett Ferres over the line with him for his second try in as many home appearances while England winger Ryan Hall proved just as unstoppable from 10 metres out after taking Joel Moon's pass.
Sinfield's touchline conversion made it 18-0 but it was a flattering score and, with a decent amount of possession, the Giants began to pose problems for the Leeds defence.
Scrum-half Jamie Ellis, who was prominent for the visitors, jinked his way over for their first try on 29 minutes and six minutes later centre Joe Wardle took hooker Shaun Lunt's short pass to crash over for a second.
Danny Brough added both conversion to cut the deficit to just six points at the break but Huddersfield were stunned by a spectacular 40-metre try by Tom Briscoe within a minute of the restart.
Substitute Mitch Achurch began the move, slipping the ball nicely out of the tackle to second rower Steve Ward, who evaded the Huddersfield defence long enough to get Briscoe haring for the corner with a deft one-handed pass.
Sinfield was off target for the first time as the Rhinos led 22-12 but, with Brough coming into the game more, the Giants came right back at their hosts.
The officials missed a clear forward pass in the build-up but winger Jermaine McGillvary maintained his composure to keep the ball alive and substitute Kyle Wood was on hand to touch down Leroy Cudjoe's grubber kick to the line.
Five minutes later the scores were level when England forward Ferres took Brough's pass and twisted out of the tackle of Hardaker to score his side's fourth try - and Brough's fourth goal put his side in front for the first time.
The lead lasted only seven minutes as Aiton burrowed his way over from dummy half shortly after Leeds were fortuitously awarded a scrum when the ball ricocheted into touch off Cudjoe.
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