Soward doubled the host's lead with his first try since round 26 of last season after a good break and offload from Brett Morris found the axed NSW five-eighth who sprinted through to score under the posts.
Souths finally woke up and started to play in the latter part of the first half with Reynolds growing in confidence and they were rewarded by a try from Sam Burgess on the half-hour mark,
The big Englishman powered his way over from five metres, brushing aside Jake Marketo for his second try of the 2012 campaign.
And on the stroke of halftime the Rabbitohs levelled the scores after great work from Matt King to gather a high kick from Issac Luke and hand off to the advancing Reynolds who raced home for his first NRL try.
The second half followed a similar pattern with the Dragons taking the early initiative with a Matt Cooper try out of dummy-half, but it was Souths who looked the brighter side after the break.
They were rewarded for their inventiveness after 61 minutes when Andrew Everingham continued his brilliant rookie season with his ninth try in just eight games.
Debutant Justin Hunt thought he had won the game with a try in the left corner, but his foot brushed the line and with Soward failing with a penalty and two field goals, the game went into golden point in front of a crowd of 14,894.
-AAP