Mount's blindside flanker Matty Axtens reduced the deficit to just two points at the opening of the second half with all the poise of an outside back.
After incisive play from Zane Butler delivered quick ball to the left, Axtens summed up the situation before going to the line with the ball in two hands.
A show and go followed, with Axtens dotting down under the sticks without a hand being laid on him. The conversion made it 12-10 and forced Greerton into another gear.
Brendan McKeown crashed over from close range to extend the lead to 17-10, before three successive penalty goals to Andrew Boyd stretched the lead to 26-10 on the hour mark.
That sparked a mini resurgence from the Mount, with Butler charging over for an unconverted try in the corner to make it 26-15. Despite a late driving try to Duncan Walker and a pair of Greerton players being shown yellow cards, the home side hung on to record another win. Parker was thrilled with the result that solidifies his side's place in the top four.
In other action, Whakarewarewa beat Rangataua 34-18, Te Puna won 38-30 against Rotoiti and Opotiki thumped Paroa 41-11. The top three sides all had good weekends in division one. Unbeaten sides Rangiuru and Poroporo beat Ruatoki and Waikite respectively, while third-placed Kahukura beat Te Teko 32-17.
Fourth-placed Ngongotaha were soundly beaten by Katikati, going down 35-15 and slipping out of the last semifinal spot. Marist St Michael's upset fifth-placed Whakatane Marist 22-3 to form a logjam in the middle of division one.