The Welsh region had the ideal start, attacking from clean line-out ball deep in Sharks territory.
Connor, the Dragons' fifth captain this season, took on the defensive line from fly-half.
The experienced 10 glided past opposite number Hodgson and stretched out to score under the posts despite a tackle from Luke Abraham.
Connor added the conversion but missed a penalty as two Hodgson kicks reduced the gap to a point.
The home side clung doggedly to their narrow lead, but were reduced to 14 men when hooker Duane Goodfield was sin-binned for a spear tackle on Hodgson - a decision hotly contested by the Rodney Parade crowd.
The Sale fly-half missed the resultant penalty, though, and Connor extended the lead with his first successful three-pointer soon after the break.
Wales scrum-half Dwayne Peel came on for the final quarter
The Sharks turned to their bench for a boost and were rewarded with Hodgson's third penalty in the 56th minute.
The Dragons fired back with a concerted attack, crowned when ex-New Zealand scrum-half Lee sneaked over from a ruck underneath the posts for a try converted by replacement fly-half Greendale.
Sale brought on Wales scrum-half Dwayne Peel in time to witness a stunning 40m break from Dragons centre Rhodri Gomer-Davies, his run going unrewarded when Greendale missed a simple penalty.
The youngster soon had the chance to make amends, though, when Koyamaibole was yellow-carded for coming in offside at a ruck, Greendale firing over a fine penalty.
Torrential rain in the closing minutes added to the Sharks' misery, but they waded to the Dragons line where they encamped for the closing five minutes.
The home side's defences were not to be breached, though, heroic tackling keeping out the fancied Guinness Premiership side.
Dragons coach Paul Turner: "We decided to use this tournament as an opportunity to develop our younger players.
"We were playing against a full-strength Sale team so we're really pleased.
"There were a lot of errors, but with that came our ability to put it right.
"Winning breeds confidence and we'll gain momentum from that."
Sale coach Kingsley Jones: "We underestimated the Dragons, a lot of sides do. We just didn't turn up - seven points down in the first few minutes and the writing was on the wall.
"No excuses, we didn't want it as much as the Dragons, it was a terrible performance on our part.
"Both sides know that with the quality of players in our 22 it should have been enough to get a win.
"Their execution was better than ours and they wanted it more. We have got to learn quickly because that is not acceptable."
Dragons: M. Thomas, Harries, Gomer-Davies, Watkins, Fussell, Connor, Lee, Watchurst, Goodfield, Palmer, Sidoli, A. Jones, MacDonald, Harris, Webb. Replacements: Andrew Brown for James Harris (42), James Harris for Andrew Brown (47), Hugh Gustafson for Dan Watchurst (60), Peter Bracken for Pat Palmer (60), Adam Greendale for Shaun Connor (62), Toby Faletau for James Harris (66), Matthew Pewtner for Martyn Thomas (72), Alex Walker for Danny Lee (74), James Thomas for Grant Webb (77).
Sale: MacLeod, Cohen, Bishop, Thomas, Vakacegu, Hodgson, Wigglesworth, E. Roberts, Schwalger, Forster, Schofield, Cox, Gaskell, Abraham, Fearns. Replacements: Neil Briggs for Mahonri Schwalger (40), Mathew Tait for David Bishop (47), Sisa Koyamaibole for James Gaskell (51), Martin Halsall for Jack Forster (58), Dwayne Peel for Richard Wigglesworth (65), Kristian Ormsby for Carl Fearns (65), Rob O'Donnell for Eifion Lewis-Roberts (74).
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.