Needing a converted try to win with time up on the clock, the Blues hammered away at the line until their inspirational captain sealed the victory.
The win puts Moana sixth on the Super Rugby Pacific table, while the Blues, the defending champions, are now seventh on the table.
Down by three at halftime, Moana surged home with a hat-trick to winger Kyren Taumoefolau — who was electric on the left wing — to keep their playoff hopes alive.
Moana first five Patrick Pellegrini banged over four penalties in the victory.
The Blues had tries to Patrick Tuipulotu and Hoskins Sotutu, and a penalty try.
Moana coach Tana Umanga and Savea fought hard to contain their emotions as they described what the victory meant.
"We heard a lot of things after the last game and we had a talk about it, how we motivate ourselves," Umaga said.
"We heard some of the narratives coming out of their camp around things.
"Ardie talked to me and said we look to the light and be the light, and I think tonight we shone bright."
Umaga said the players had built a lot of self-belief and faith, trusting their processes and one another, which helped them get the win.
"For us, I think we just stuck to the plan," he said.
"We had a lot of belief. This week we prepared really well and we’ve just been building throughout the season.
"We knew these three games are going to be tough for us.
"Our guys are really growing and I know they will grow again."
The Fijian Drua had a big 38-7 win against the Western Force in their last home game of the year in Lautoka.
Sio Tomkinson scored in the opening three minutes for the Force to go up 7-0 early.
But the Drua piled on 38 unanswered points — and led 17-7 at the break — to secure the victory.
In Australia, it took the Brumbies until the 47th minute to break the deadlock against the Reds.
With the game level 7-7 at halftime, the Brumbies surged ahead through Andy Murihead’s try to eventually win 24-14.
The Brumbies are top of the table on 43 points. — RNZ/APL
