The Rhinos trailed 16-8 at halftime on Thursday's (Friday AEST) despite bossing much of the first 40 minutes in the teams' first meeting since Saints' astonishing smash-and-grab in last year's play-off eliminator at the same venue.
But with the wind at Leeds' backs in the second half, Harry Newman's try was converted by Jake Connor, who added two penalties before forme Parramatta winger Maika Sivo touched down in the closing stages, when Saints were down to 14 after David Klemmer was sin-binned.
The win was just Leeds' third in 24 meetings against one of their biggest rivals and took them ahead of the Warrington Wolves, who have played two games fewer, and Saints, who have lost for the fourth time on the road this season.
Following a poignant pre-match tribute to league legend and broadcaster Jon Kear, who died on Sunday, Alex Walmsley pointed to the sky after dotting down in commemoration of his former Batley coach, having dashed over from the fleet-footed Daryl Clark's offload.
Saints, though, switched off in the 27th minute, allowing Chris Hankinson to score on his 100th Super League appearance, but having fought tooth-and-nail to establish an 8-6 lead, the hosts fell behind again after half an hour.
Jake Connor had openly celebrated in front of Saints fans after Hankinson scored but he was left eating humble pie when former North Queensland flyer Kyle Feldt gave it back to him after barrelling through the Leeds man to score.
Jack Welsby's grubber then sat up perfectly for ex-Dragons and Broncos back Tristan Sailor to slide home on his knees on the opposite flank as Saints went in 16-8 ahead, but Leeds rallied to level soon after the resumption.
Harry Newman dived over from a bullet pass from Brodie Croft, another ex-NRL star with Melbourne and Brisbane, with Connor adding the extras and then his second penalty of the evening with half an hour left after Kallum Watkins was taken out high.
The decisive moment came with six minutes left when Hankinson was cleaned out too late by veteran Klemmer, who was subsequently yellow carded, with Connor booting the resulting penalty.
Saints finishing a man down was exploited in the 78th minute as Sivo bagged his 20th try of the season on the left, with Connor converting to finish with a dozen points.
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