The Manchester side ended the game with 10 men as Michael Donohue was red-carded in the 50th minute.
Sixty seconds later the Magpies went ahead, Newby scoring the opening goal.
It stayed that way until the 76th minute at Victory Park, when Newby doubled his – and Chorley’s – tally by netting the second.
O’Keefe then added gloss to the scoreline with two more strikes in the 79th and 83rd minutes to put Jamie Vermiglio’s side back on top of the National League North.
They have a game in hand over morning leaders Bradford Park Avenue, who slipped up at home to Guiseley.
Elsewhere in the division, Southport held hosts Chester to a goalless draw.
In the National League there were also no goals as AFC Fylde shared the points with visitors Barrow.
And in the NPL Premier Division, Bamber Bridge lost 2-0 at Warrington Town.
Connor McCarthy got both goals as the home side made it seven wins on the spin and an unhappy start to the year for Brig boss Mick Taylor.
Lancaster City were also beaten, 3-1 at Marine.
Glenn Steel put the Dolly Blues in front after 21 minutes.
But it all went downhill after that, Steel putting through his own goal to level the scores, then Charley Edge (75) and Niall Cummins (88) making the points safe for the Merseyside outfit.
In the NPL West Division, Kendal’s Scott Harries rescued a point in a 2-2 home draw with Clitheroe.
Harries opened the scoring in the 14th minute but Clitheroe hit back through Max Hazeldine (22 and 74) and looked like going on to win.
But a minute from time, Harries made it 2-2.