But they were also helped by several key injuries to opposition players.
Leeds full-back Brent Webb was unable to start the game after suffering a back spasm while scrum-half Rob Burrow and centre Clinton Toopi were struck down during the match.
The influential Burrow was helped off with concussion midway through the first 40 minutes when he went in head first on a tackle on Lee Gilmour.
By that stage, Leeds were a try and conversion down after a thrilling burst from Long led to a simple score from the obliging Flannery.
Reaction: Leeds 16-26 St Helens
Leeds captain Kevin Sinfield was largely quiet in the first half but got two points on the board from a penalty.
But just as Brian McClennan's side were beginning to mount a fightback, the team were hit by injury again when Toopi was left clutching his knee after making a tackle near his own tryline.
St Helens took full advantage of the situation when Long made use of the clever dummy run of Gilmour to feed mammoth stand-off Pryce, who strode through from 15 metres.
Long converted to give Daniel Anderson's men a 12-2 lead going into the break - and that advantage was extended thanks to an extraordinary effort from Francis Meli.
The Kiwi cut in from the left, eluded two tackles before finding Gilmour, who offloaded for Wilkin to canter in under the posts.
It seemed that Saints would run away with the match, but Lauitiiti had other ideas.
The second-rower, who was earlier seen encouraging his team-mates, powered over from five metres, with Sinfield converting to cut the gap to 18-8.
Moments later, Donald found the left corner from Keith Senior's pass, having earlier been denied a score from a yard out.
After Sinfield had missed the conversion, Leeds made yet another error in front of their posts, allowing Long to strike his penalty from dead centre to extend the lead to 20-12.
The Rhinos were made to pay again 10 minutes before the end when a lapse in concentration 10 metres out allowed 22-year-old prop Bryn Hargreaves to fly over.
New Zealand-born Kylie Leuluai went over late for Leeds but it could not prevent Saints from booking their place at Wembley, where they will face either Hull FC or Wakefield.
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