Before Davids had clinched the match for the Kimberley visitors at Wits University, the home team held a slender 17-16 lead after they had managed to wipe out a halftime deficit of 3-13 thanks to a spirited second-half performance.
But unfortunately the Sigma Lions, now winless after eight games, had an indifferent first half during which they conceded far too many penalties.
The men from Kimberley went into halftime with a 10-point advantage having scored the only try of the opening half, a conversion and two penalty goals, while the home side replied with one penalty goal.
Experienced Windhoek Draught Griquas flyhalf George Whitehead slotted a penalty goal for the first points of the game following a penalty against the Sigma Lions for an illegal tackle.
The first try of the afternoon also went the way of the visitors and it came against the run of play when they forced a turnover deep inside their own 22. The ball was worked to the right, where former Maties speedster Munier Hartzenberg showed his pace to run in under the posts.
Whitehead then added his second penalty goal as he made the home team pay for their transgressions, while Tiaan Swanepoel (fullback) put the hosts on the board with a penalty goal.
Whitehead got the first points in the second stanza with another successful penalty goal as he stretched the visitors' lead to 16-3.
But the Sigma Lions came roaring back with two converted tries, by Swanepoel and Boldwin Hansen (right wing), which gave them the lead for the first time with the score on 17-16.
However, the visiting side kept cool heads as they managed to string together 15 phases to score the winning try through Davids. Whitehead - who was shown a yellow card 10 minutes earlier - returned just in time from his period in the sin bin to take the conversion and leave the home team and their fans heartbroken.
Sigma Lions 17 (3) - Tries: Tiaan Swanepoel, Boldwin Hansen. Conversions: Swanepoel (2). Penalty goal: Swanepoel.
Windhoek Draught Griquas 23 (13) - Tries: Munier Hartzenberg, Ashlon Davids. Conversions: George Whitehead (2). Penalty goals: Whitehead (3).