Eksteen’s contribution came through a try, three conversions and six penalties as the fullback consolidated his position as the season’s second highest point scorer.
The visitors, who ended third on the log, opened up a 12-0 lead within the first six minutes through tries by Eksteen and flanker Wayne Khan.
Both sides traded a few penalties before the Griffons landed their first try through flanker Martin Sithole, which right wing Nico Scheepers converted to bring the home side to within two points halfway through the first half.
The Eagles extended their lead to seven points when winger Carlo Radebe scored in the corner but the home side retaliated immediately to level the scores fullback Wayne Pienaar went over for a converted try.