Joynt's powerful running set up two tries in the first half and he then killed off Leeds' revival in the second by charging on to Paul Newlove's pass to score the one that effectively decided it.
If ever there was a turning point in a match this was it, with Saints apparently flagging one moment but then adding further tries through Anthony Sullivan, Fereti Tuilagi and Chris Smith to win with deceptive ease and set up a match next week at Bradford that will see the winner go straight into the Grand Final.
Saints' ability to seize their try-scoring chances gave them a marvellous start. Joynt has had an excellent season and he was the architect of their two tries in the first 10 minutes.
It was his run that was stopped on the line by Darryl Powell's tackle, but that only allowed Newlove to plough over from close range.
Joynt then took Tommy Martyn's short ball to crash through again, this time serving up the pass for Sullivan to score his first in the corner.
Leeds were so off colour that Saints could have had more, notably when Newlove threatened to intercept and go the length of the field, only to be stopped by Andy Hay's high tackle.
Justice of a sort was done soon after, with Saints going upfield and Tuilagi and Kevin Iro creating the chance for Smith to score wide on the right.
Martyn missed all three conversions, as he did a drop goal attempt before half-time. An unhappy half for him reached its low point when he came out of the defensive line looking for an interception from Ryan Sheridan and left a huge gap for Iestyn Harris to score at will.
Harris' conversion, added to an earlier penalty, left Leeds only four points behind at the break. Saints nudged further ahead when Martyn finally succeeded with a kick and Newlove claimed his second try after Paul Sculthorpe's drop goal effort was charged down.
When Lee Jackson chased his own kick to touchdown, Leeds were right back in contention, but Joynt's try triggered a remarkable collapse, leaving Graham Murray with much to do before their meeting next week with the winners of Sunday's game between Wigan and Castleford.
St Helens: Atcheson; Smith, Iro, Newlove, Sullivan; Sculthorpe, Martyn; Perelini, Cunningham, O'Neill, Clark, Nickle, Joynt. Substitutes used: Tuilagi, Hoppe, Matautia, Wellens.
Leeds: Harris; Rivett, Godden, Senior, Cummins; Powell, Sheridan; Masella, Jackson, McDermott, Morley, Farrell, Glanville. Substitutes used: Hay, Matthiou, St Hilaire, Sinfield.
Referee: S Presley (Castleford).