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The visitors took the lead in the sixth minute when James Roby managed to burst through three tackles and touched the ball down under the posts. Luke Walsh added the conversion from close range to put his side 6-0 ahead.
Leeds had the opportunity to hit back immediately as Lee Briscoe broke away down the right following a flowing team move and he reached out for the line to get the ball down. However, replays showed that he lost control of the ball at the final moment, which chalked off his effort.
The Saints extended their advantage when they were awarded a penalty right under the posts, and Walsh held his composure to slot his kick through to take his side's lead to eight points.
However, the Rhinos came back into the match as they capitalised on a penalty to drive themselves right to the edge of the tryline. Their pressure paid off as Zak Hardaker crashed over the line and Kevin Sinfield added the conversion to reduce the deficit to two points.
Sinfield notched his second kick of the game to tie the scores, but Walsh added a drop goal just before half time to hand the Saints a narrow advantage.
In the second half, Carl Ablett thought that he had put his side ahead when he touched down over the line, but his score was ruled out as he was short of the line.
Saints extended their lead in the 60th minute when Mark Percival raided down the right and collected an offload before racing over the line to touch down for the score. However, Walsh missed his first kick of the night.
The miss proved to be crucial as Leeds came back at the visitors and found the tryline for the second time of the night as Ryan Hall twisted through a tackle and just managed to ground the ball, while Sinfield added the crucial extras to put his side ahead.
Leeds secured their berth in the final when Walsh tried to keep Saints' slim hopes alive with an ambitious pass, but Kallum Watkins seized on the ball and ran in for the simple score and Sinfield slotted the kick through the posts to send his side to Old Trafford.
The Rhinos will face off against Wigan Warriors to compete in the final for the first time since they lifted the trophy in 2012.