But former Steamers captain Willie Ripia, who was at fault for one of Greerton's tries, scored a try and converted following some nice build-up play by Rotoiti. He then kicked a 50m penalty to push Rotoiti out to a seven-point lead.
Greerton hit back with a try late in the game but missed the conversion from the sideline.
New Rotoiti player Chanse Perham then scored a last minute try to confirm the result for the home side.
Earlier tries to Perham, Joe Royal and Lionel Skipworth ensured Rotoiti grabbed a bonus-point victory.
Rotoiti vice-captain Royal said he was proud of his team.
"In previous years we have not been able to close out games or come back from a deficit so I'm proud of the boys' efforts," he said.
"I think we were able to stick to our structures today and pull off some classy moves from our backs but I think our forwards did some hard yards, so all in all it was just a good team effort."
He said Rotoiti knew they had a good side this year but did not want to get too far ahead of themselves. Rotoiti also won the Central Bay of Plenty local round last month, to add to their growing confidence.
Steamers player Siegfried Fisiihoi, who injured his shoulder last year, made his return off the bench for Rotoiti.
Rotoiti now have a run of three tough fixtures including Tauranga Sports (away), Te Puke (home) and Mount Maunganui (away).
Meanwhile, the other premier matches in Rotorua were more one-sided on Saturday.
Whakarewarewa got off to a great start this season running up a big score against Paroa, winning 91-7, while Waikite battled hard but lost to Whakatane Marist 58-13.
The Baywide premier and division one competitions include 12 teams each this year and will include a full round-robin before the playoffs.
Baywide rugby results (round one):
Premier: Whakatane Marist 58 Waikite 13, Whakarewarewa 91 Paroa 7, Te Puna 47 Rangataua 7, Rotoiti 34 Greerton Marist 25, Tauranga Sports 62 Opotiki 10, Te Puke Sports 22 Mt Maunganui 12.
Development grade: Whakatane Marist 29 Waikite 17, Whakarewarewa 28 Paroa 10, Te Puna 70 Rangataua 10, Greerton Marist 36 Rotoiti 10, Tauranga Sports 12 Opotiki 5, Te Puke Sports 24 Mt Maunganui 19.
Division One: Kahukura 16 Ruatoki 12, Judea 38 Katikati 17, Arataki 10 Marist St Michael's 3, Rangiuru 38 Galatea 7, Ngongotaha 22 Reporoa 12, Te Teko 62 Poroporo 13.