The Kimberley-based side ran in seven tries to accumulate the full five points and now find themselves six points above the second-placed Leopards, who had a bye this weekend.
Elsewhere on Saturday, a two-try burst by the SWD Eagles saw them secure a hard-fought 21-17 (half-time 7-10) victory over hosts, the Boland Cavaliers in Wellington.
The Cavaliers were looking to record a second victory in the qualifiers after thumping Border 37-12 the previous Saturday. SWD had been on the receiving end of a 52-34 hammering from the Falcons at Outeniqua Park in George and needed to bounce back strongly.
In the remaining match, the Falcons turned in a superb second-half performance on their way to a 54-40 (half-time 12-26) victory over the Border Bulldogs at the Barnard Stadium in Kempton Park.
Border made a strong start and the home team was staring down the barrel trailing by 21 points soon after halftime. But led by 21 points from fullback Juan Kotze, the Falcons scored 28 unanswered points in an impressive finish to secure their second win of the campaign.
After Saturday's round of matches, Griquas lead the log standings with 18 points after four matches, followed by Leopards on 12, the Falcons and SWD Eagles (both 10), Boland Cavaliers and Griffons (both 7) and Border Bulldogs (1).