The Saints started brightly with both Aeron Edwards and Sam Finley testing the home goalkeeper.
Midway through the first half the New Zealand International, Greg Draper fired just over, after meeting a brilliant cross by former Wrexham man, Simon Spender.
Soon after, Draper raced clear and despite lobbing the ‘keeper, the ball landed on the roof of the net to ensure that the teams went into half time level.
After a goalless first half, Craig Harrison brought on Matty Williams and Alex Darlington to replace Aeron Edwards and Greg Draper.
With half an hour left, Finley did well to set up Williams and the former Notts County man just missed with a superb curling effort.
Moments later Williams broke the deadlock after latching on to a fantastic cross from Ryan Fraughan, before stabbing into the net.
The Oswestry side dominated the remainder of the game and the match finished Cliftonville 0-1 TNS.
The starting line up for TNS was Paul Harrison, Simon Spender, Chris Marriott, Phil Baker, Kai Edwards, Aeron Edwards, Chris Seargeant, Sam Finley, Jamie Mullan, Ryan Fraughan and Greg Draper.
On the bench for The Saints were Chris Mullock, Alex Darlington, Matty Williams, Connell Rawlinson, Scott Ruscoe, Aaron Simms and Scott Quigley.