The 26-year-old Reynolds laid on three first-half tries with grubber kicks behind the Warriors' defence, also kicking a field goal and landing five from six conversions.
The half-back was subsequently hauled off in the 46th minute with a hamstring injury.
The Warriors, who entered the match as strong favourites, drop to ninth on the ladder and will rue missing the opportunity to cement themselves in the top eight.
Souths will take confidence from their performance in what has been a disappointing 2016 campaign.