Waiheke made a couple of chances themselves with Tommy Pamment holding fast in goal.
Defenders Ray How and Ben Donald were tight in the middle while Andy Smith and Yago Zavoluk dealt with the wide players as they tried to use their pace to get in behind.
O'Reagan's red card as the second half started made Tauranga's job more difficult and soon after Ramiro Cabeza Villar put the visitors ahead 1-0.
Tauranga held them out for 15 minutes but two quick goals from Marc Evans and a second to Cabeza Villa sealed the win for Waiheke.
The loss leaves Tauranga City in eighth place on the table and needing points to move away from the relegation zone.