The second spell began with the Eels bombing a great chance in the opening set but the ever reliable Weedon then showed his class, stepping off his left foot through the defensive line, to put the Eels ahead in the topsy turvy encounter.
The game was tied up yet again with 20 minutes left when the Eels markers went to sleep on their line, gifting a simple try to Harley Randle.
The Tigers will rue going for goal from wide out, which missed, when they had the Eels trapped in their own red zone. It cost them dearly, as Jesse Muller made a strong surge upfield to win a crucial penalty, which Weedon converted to win the match.
Eels coach Jock Nicholson says his senior players, particularly Weedon, Tarquin Court and Willz Rutene, stepped up when it really mattered.
"To be fair the Tigers played awesome and I haven't seen a game like that in a long time," Nicholson said.
"I look forward to the final next week. There is always something you can work on and improve. For us, if you can control the possession for the majority of the time, you win the game, and that is what we need to do consistently."
The Eels will play Taniwharau at Davies Park in Huntly on Saturday, who they narrowly lost to 26-28 a week ago. Otumoetai Eels 20 (Tane Leef, Tarquin Court, Josh Weedon tries; Weedon 4 goals) Hamilton City Tigers 18 (Erura Keepa 2, Harley Randle tries; Vaughan Calcinai 3 goals)