A yellow card to first five-eighth Otere Black in the dying stages of the first half put the Māori All Blacks further on the back foot, as they headed into the half time break facing a 12-point deficit.
The differential in time on the football showed in the starts, with more than 70 per cent of the half played in the Māori All Blacks end of the park, with the side missing 21 tackles to Fiji's one in the first 40.
With Black on the sidelines for the first seven minutes of the second half, Fiji made the most of the one-man advantage with Nayacalevu crossing for his first try and Volavola kicking a conversion and a penalty to accumulate a point for every minute Black was in the sin bin. Two tries to left winger Sean Wainui gave the Māori All Blacks some hope late in the contest, but Fiji proved to be too good and sealed their eighth-straight win in Suva.
"We really struggled in that first half to really make our tackles," Māori All Blacks captain Ash Dixon said. "The Fijian boys played some awesome footy and their offload game was pretty good.
"We didn't really exit that well either so we gave them some good opportunities with ball in hand and we couldn't apply any pressure ourselves. So it was really disappointing for us, we've got a lot of things that we need to get right.
"We've got a fair bit to work on. I'd say our defence will be one of the first things we're going to have to start with but in saying that there were some good phases there we put together and went alright, but we didn't apply enough pressure on to the Fijian side and cherish the ball enough."
The sides will meet again next Saturday in Rotorua.
Fiji 27 (Waisea Nayacalevu 2, Alifereti Veitokani, Viliame Mata tries; Ben Volavola 2 cons, pen)
Māori All Blacks 10 (Sean Wainui 2 tries)
HT: 12-0