Leeds scored a try in each half of this scrappy, spoiling tie at Headingley, but Saints effectively lost it by ignoring the insistence of their coach, Ellery Hanley, that discipline was paramount. Despite having the wind and the intermittent rain on their backs, it was not an easy first half for Leeds.
A particularly messy first 15 minutes saw them as the main transgressors, conceding no fewer than eight penalties, three of them close enough to the sticks to be swatted over by Sean Long.
One kick from Harris gave Leeds temporary parity, but they were ragged by comparison with their performance against Wigan in the previous round.
But Leeds learnt their lesson, and gradually the balance of play began to swing in their favour, two more penalties from Harris bringing them level and settling them down sufficiently to play some rugby.
A first try of the match was in prospect when Harris' pass sent Daryl Powell through, but Paul Atcheson's tackle saved the day.
On 33 minutes, they made their breakthrough, Ryan Sheridan starting the move with his pass to Jamie Mathiou and then looping round to take Marc Glanville's long ball, out-flanking the Saints' defence to score.
Harris, immaculate as ever, put over his goal from the touchline and only just failed with a penalty from halfway soon after.
Two minutes before the break Leeds were again within inches of extending their lead, Chris Smith's tackle doing just enough to take Francis Cummins' foot into touch before he could touch down.
Harris did stretch the lead after the break when he was blatantly taken out by Sonny Nickle after kicking through.
Lee Jackson and Nickle both went to the sin bin as the result of separate incidents as the referee, Stuart Cummings, finally lost patience with the amount of messing and mauling that was going on. In between , Paul Sculthorpe thought he had scored for Saints but Tommy Martyn's pass had been clearly forward.
They finally got their try after 49 minutes, Long and Martyn linking well for Vila Matautia to find Kevin Iro, whose pass allowed Paul Newlove to fend off Harris. Long could not land the conversion, but Harris made no mistake with another penalty to add to Leeds' score.
Fittingly, it was yet another penalty that gave them a match-winning lead, Matautia's swinging arm giving Harris a simple seventh goal.
Seven minutes from the end, Sheridan and Tony Farrell sent Terry Newton over, Harris kicked his eighth goal and Leeds, without ever touching the height of a fortnight ago, were safe, Atcheson's injury-time try for Saints making no difference.
Hanley, back on a groud he graced as a player, had no illusions about where it had gone wrong. "We were very indisciplined right across the paddock and that was our downfall," he said. "Leeds cleaned their act up and that was the deciding factor."
Leeds: Harris, Rivett, Blackmore, Godden, Cummins, Powell, Sheridan, Masella, Newton, Fleary, Morley, Farrell, Glanville. Substitutes used: Mathiou, Jackson, Hay, St Hilaire.
St Helens: Atcheson, Smith, Stewart, Newlove, Tuilagi, Martyn, Long, O'Neill, Cunningham, Davidson, Perelini, Nickle, Sculthorpe. Substitutes used: Iro, Adamson, Matautia, Wellens.
Referee: S Cummings (Widnes).