Rhinos produced an attacking masterclass in the first half and then a spirited defensive display after the break to record their sixth straight win and 10th in 11 games.
Leeds played breathtaking rugby in the opening period, scoring five tries to go in with a 28-6 lead.
It was a different story for much of the second half as the hosts came out fired up and put Rhinos under huge pressure.
The conceded two tries, but Saints never quite got close enough to really set nerves jangling among the noisy travelling support and Leeds scored a couple of late touchdowns to ‘win’ the period 13-10.
It was a night to remember for 19-year-old winger Ash Handley, who scored a brilliant first-half hat-trick.
And hats off to coach Brian McDermott, who made some bold selection decisions which paid dividends.
There was only one change to Rhinos’ 17 from the win at Salford five days earlier, but a series of shocks in the way Leeds lined-up.
Kallum Watkins returned from illness and replaced Ashton Golding, but he started out of position on the right-wing, outside Carl Ablett, who continued in the centre.
Handley switched to flanks to the left-wing and Zak Hardaker was at full-back.
Liam Sutcliffe, a substitute last week, started at stand-off, alongside Danny McGuire and Rob Burrow dropped to the bench.
Adam Cuthbertson was back in the starting front-row, Brad Singleton moved to loose-forward - as an extra prop - and Kevin Sinfield was on the bench, for the first time since 2003.
Brett Delaney started in the second-row,swapping places with Mitch Achurch, who was among the substitutes.
It seemed, to paraphrase Eric Morecambe, a case of all the correct players, though not necessarily in the right order – but it worked.
Sutcliffe was magnificent in the first half and scored the try which ended Saints’ fightback in the second.
There was another huge effort from Stevie Ward and Singleton and Joel Moon also had big games in another fine team effort.
Rhinos – who have four first-choice players on the casualty list – went ahead in spectacular fashion inside three minutes. Saints were pounding the line, following Jamie Peacock’s high shot on Alex Walmsley.
McGuire made a try-saving tackle on Jordan Turner on Saints’ left, but the hosts moved the ball right and looked set to score when Josh Jones aimed a pass at Matty Fleming, only for Handley to intercept, knock the ball in the air, regather and race 80 metres for his third try in as many games.
Leeds could have scored again when Singleton’s pass to Zak Hardaker opened up the defence, but there was no support and Tommy Makinson – playing at full-back for Saints – stood his ground to make the tackle.
Mark Flanagan then threatened to go clear from near his own line, but Hardaker made a crucial stop.
That was a rare opportunity for Saints, who spilled the ball three times coming away from their own line in the opening quarter.
On 16 minutes, Leeds received back-to-back penalties, the second close to the line in a kickable position. They opted for a tap and superb goalline defence kept Stevie Ward and Paul Aiton out.
Cuthbertson then fed Joel Moon and he did brilliantly to beat the first defender,draw the second and flick out a pass to Handley, who got over at the corner and had the presence of mind to narrow the angle for the conversion.
In the set from the re-start Sutcliffe, went on an arcing run, got past Jon Wilkin and cut infield before timing his pass perfectly to the supporting Hardaker.
Sutcliffe’s third conversion made it 18-0 after 19 minutes.
Sinfield came on after 25 minutes, in place of Cuthbertson, playing at loose-forward. Within three minutes he was adding to his personal points tally by converting Rhinos’ fourth try.
Saints tried to hammer Leeds near the visitors’ line, but they overdid it and Ablett spotted a gap, broke into open space and then fed McGuire, who had the pace to hold off the defence from inside his own half.
Saints got back into the game with an extraordinary stroke of luck just before the break.
Wilkin kicked ahead, Maskinson seemed to knock-on, but followed up and was able to touch down at full-stretch.
Referee Ben Thaler said no try and the big screen replay seemed to back that up, but the video refs – Richard Silverwood and Warren Turley – gave it anyway and Travis Burns converted.
Saints sensed a comeback and there was another try before the break, but Leeds scored it.
Watkins intercepted from Makinson close to Rhinos’ line and made it to 20 metres out from the other end, before Fleming ran him down.
The Leeds man showed great composure to hang on to the ball and on the next play Sutcliffe cross-kicked to the far corner and Handley made a brilliant touch down for his first senior hat-trick, as the hooter sounded.
Luke Walsh, Saints’ inspirational half-back, came on at the start of the second half and created a try within five minutes, breaking up the middle and slinging out a wide pass which was finished by Turner.
Cuthbertson and Hardaker held Walmsley up over the line, Peacock and Ward made key tackles on Burns and Ward held Mose Masoe up over the line before on a final tackle play, Turner scored his second from Walsh’s kick and Burns’ second goal cut the gap to just 12 points.
That try came in the set after Hardaker had spilled a kick.
Like Leeds in the first half, Saints were harried into a number of errors inside in their own territory, while the home team – despite chasing the game – handled much better.
Rhinos only had one second half attack until the 67th minute, but when they finally got a chance, they made sure they took it.
It was another top-class score, Peacock and Cuthbertson off-loading before Sinfield picked the ball up off the floor and shipped it on to Sutcliffe, who stepped a couple of times and then cut through to score close enough for Sinfield – on for his second spell – to convert.
Four minutes later Sinfield booted a last tackle drop goal and Moon crossed on the final play of the game, from a Saints error, Sinfield converting to seal a famous win.
The penalty count finished 5-3 in Leeds’ favour (2-2 in the first half).