Geyser bowled first in their match at Smallbone Park and had Greerton in trouble at 168/7 after 31 overs. However, a brave bottom-order bash saw Greerton score another 111 runs in the remaining nine overs to finish their innings at 279/9.
In response, Geyser could manage only 218 all out after 38.1 overs.
Batting at number three, Sam Kelly top scored for Geyser with 63 runs.
He was helped by brother Liam, who scored 27, but in the end it was not enough to rescue Geyser from defeat.
Eight teams will now contest the second round of the McNaughton Trophy on February 17, including Rotorua's Central Cricket Club and Taupo Wanderers Cricket Club.
The competition holds a rich significance in second-tier cricket, with reserve grade teams given a chance to make a name for themselves.
The origins of the Baywide reserve grade prize come from the donation by the McNaughton family in Te Puke.
At first, the trophy was offered only to second-tier teams from the Tauranga and Te Puke sub-associations.
However, a change several years ago saw the competition expanded to include all reserve grade sides in Bay of Plenty cricket.
In the past two seasons, Mount Maunganui have beaten Katikati twice to lift the trophy. In 2010, Rotorua's Central Cricket Club made the final but lost to Katikati.