With both sides struggling to hold onto the football, Reddy scored his second try five minutes before halftime with Greg Inglis throwing the final pass as he did for Souths' first try.
Gerard Beale gave the visitors some hope just before the break when he scythed over out wide for the Rabbitohs to enjoy an 18-4 half-time lead before 11,771 fans.
The contest again struggled to reach any great heights after the resumption before Souths scored two tries in seven minutes between the 62nd and 69th minute.
First Adam Reynolds regathered his own kick close to the line before Dylan Walker stepped his way over for Souths to cruise to a 28-4 advantage.
Tyson Frizell restored some credibility for the Dragons when he crashed over in the 69th minute when Gareth Widdop batted down a Benji Marshall kick.
Reynolds slotted over a field goal 10 minutes from time.
In and around the ruck remains the Dragons' achilles heel with the Burgess boys - Sam, George and Tom - all racking up big metres.
McGregor experimented with Josh Dugan in the halves and while he didn't present a compelling case to slot into Josh Morris's NSW spot for State of Origin II, he tried hard throughout.
Marshall again struggled for the Dragons throwing a number of poor passes before producing a no-look flick pass when in the clear late in the game to Jason Nightingale before the movement broke down.
Late in the game Dragons hooker Mitch Rein was put on report by referee Shayne Hayne for a dangerous throw on Tom Burgess.
Coach Michael Maguire said Souths set up the win with a clinical first half.
"I thought in the first half we were quite thorough. We were coming together with our attack," he said.
"In the second half, we put a bit of pressure on ourselves."
Maguire said he was pleased with his side's 7-5 first half of the season.
"After those three losses (in a row), we have built our way out of that.
"We have put ourselves in a reasonable position but we are aware there is a lot of football to play."
McGregor said a number of soft penalties his side gave away late in the tackle count cost them - and the 7-2 penalty count - but praised the Dragons' mental toughness.
"At different times out there, we showed some character against a very classy football team," he said.
"They are a very clinical football side; they are a top four team."
"We have no excuses - we had a week together. We have a lot of hard work ahead of us."
- AAP