Against all the odds, Leeds were in the game until the final seconds when Saints’ fourth try sealed it.
That was despite Zane Tetevano being sent-off for a late challenge on Saints half-back Theo Fages just five minutes into the second half.
It was an incredible effort by patched-up Rhinos, who were outstanding in the first half and staged a dramatic comeback in the second to leave Saints - near full-strength - hanging on.
Captain Luke Gale (broken thumb), Liam Sutcliffe (knee) and Bodene Thompson (ribs) were all ruled out from the side which lost to Castleford Tigers last week, so Rhinos were without 12 senior players.
They had forwards Rhyse Martin and Cameron Smith in the halves, another second-rower, Alex Mellor, at centre and 17-year-old debutant Morgan Gannon among the substitutes.
Of the backs, only the wingers - Tom and Luke Briscoe - were in their specialist position.
King Vuniyayawa came off the bench for his debut, but lasted only three minutes before being concussed in a sickening collision with Agnatius Paasi.
It looked like being a long, painful afternoon for Rhinos when they conceded after less than four minutes, Tommy Makinson stepping inside Luke Briscoe for a worryingly easy try, off Kevin Naiqama’s pass.
The same player landed a touchline goal, but Leeds responded in style to draw level after 10. Smith won a repeat set and at the end of that Kruise Leeming slipped out a pass from dummy-half and Mikolaj Oledzkipowered over from close range.
Martin converted and the scores were level until 10 minutes before the break when Makinson booted a penalty following a high tackle by Mellor on James Bentley.
The next points came through another Makinson penalty following Tetevano’s dismissal and Regan Grace touched down moments later to extend the gap to eight points.
James Roby had a touchdown disallowed by video referee Liam Moore, overruling Thaler, but with 18 minutes to go Rhinos were penalised for offside after a Saints knock on and in the resulting set, Jonny Lomax sent Grace over.
When Makinson added the extras it seemed to be game over, but - remarkably - Leeds got back to within two points with nine minutes left.
Brad Dwyer darted through from acting-half twice, Martin converting both and a Leeds win suddenly looked possible, but in the dying seconds Grace made a break which led to a clinching try for Makinson who converted to finally end Rhinos’ hopes.