Nikki Walker came close to securing a dramatic win for the visitors only two minutes from time but had the ball wrenched from his grasp by Ben Breeze only inches short of the line.
The Dragons looked to be home and clear after building a 20-6 lead with a try from skipper Jason Forster setting their attacking tone early on.
Craig Warlow’s conversion and a 45-metre penalty by Warlow extended the Dragons’ lead to 10 points after half an hour before Charlie Hore struck the opening points for the visitors with a simple penalty five minutes later.
The Dragons’ lead was trimmed to 13-6 with Hore’s second penalty five minutes
into the second half after excellent approach play by back-row duo Wayne McEntee
and Semo Sititi.
The error count increased as the battle for supremacy intensified, with the
Dragons pressing nervously to close out the game. Following a series of abortive thrusts the Dragons engineered a superb score when Warlow delivered a neat chip into the hands of Gareth Wyatt and the flying winger touched down for Warlow to convert.
That seemed the decisive blow but the Reivers refused to throw in the towel and within three minutes Stuart Moffat sent Stephen Cranston over for a try, converted by Hore.
It became 20-16 with another Hore penalty to set up a tense finale and in a dramatic late twist Walker appeared to cross but lost the ball in the act of touching down following a magnificent last-gasp challenge by Breeze.