In an entertaining affair on a treacherous surface at The Rock, the Saints twice took the lead in the first half with a well-rehearsed set-piece move which saw Barry Haraloumbous force the ball home from Nick Jones corners.
But in-between, Aron Blackwell was allowed to run from midfield and slice through the visitors' defence for a goal against the run of play.
Charlie Proctor increased the lead with a superb 25-yard strike on 56 minutes, but the Ancients fought back to level with Blackwell beating keeper Josh Roberts in a one-on-one and Mathew Bride levelling with a 25-yard power drive.
With the game finely balanced, the Saints regained the lead 15 minutes from time when Scott Quigley flicked on a cross for Ashley Jones to bundle the ball over the line from close range.
And Quigley made the game safe in stoppage time with a fine solo effort.
The scholars face another weekend of cup action in seven days' time with home games in the NEWFA Cup against Coedpoeth (Saturday) and in the FAW Youth Cup against Llanelli (Sunday), both at Park Hall.
Photo: Barry Haraloumbous heads the second TNS goal.