Eels fullback Shay Stevens crossed after the break and with Weeden's great sideline conversion it was 26-6.
Taniwharu stormed back to close the gap to 26-24 with nine minutes left. A 40/20 gave them another chance and they scored in the corner to take the lead for the first time.
There was more drama to come with the Eels going for a short restart, but Taniwharau penalised for stopping it going 10 metres. The penalty was given 40 metres out and with the chance to tie the game, Weeden, who was five from five, dragged his shot left to end a dramatic afternoon.
There is just one semifinal spot still up for grabs with the Eels and the Taupo Phoenix - who went down 26-18 to the Hamilton City Tigers at Taupo's Hickling Park - the contenders.
The Pacific Sharks, who still have a couple of catchup games to play beat Turangawaewae 20-0 at Ngaruawahia's Paterson Park to keep them on track for a home semifinal, while United look to have got clear of the wooden spoon with a 32-22 win over the Pikiao Warriors at Rotorua's Puketawhero Park.
The Eels reserves lost in similar fashion to the premiers in their game against Taniwharau 32-26 after surrendering the lead.
Results
WaiCoa Bay Premier competition, round 16
Taniwharau 28 Otumoetai Eels 26
Hamilton City Tigers 26 Taupo Phoenix 18
United 32 Pikiao Warriors 22
Pacific Sharks 20 Turangawaewae 0