Barry Town United cut the arrears at Park Hall through Nat Jarvis, but Saints stood firm to ensure they remain five points clear of second-placed Bala Town.
Scott Ruscoe’s table-toppers have now won nine and drawn their other two league matches this season as their excellent start continues.
They are next in action when they travel to Cardiff Met University on Saturday.
Robles had already struck a post by the time he headed Saints in front in the 39th minute. Leo Smith’s corner was turned back across goal and Robles directed a header high into the net.
Saints pushed to double their advantage at the start of the second half, with visiting goalkeeper Mike Lewis saving impressively from Draper’s close range header before blocking an effort from Ryan Astles.
TNS goalkeeper Paul Harrison did well to deny Michael George ahead of the hosts increasing their lead to 2-0 in the 72nd minute.
A fine pass from Jon Routledge released Robles down the right and he pulled the ball back for Draper to confidently find the net with a first-time finish.
Barry had a goal of their own to celebrate four minutes later when Jarvis converted an inviting cross from the left from Chris Hugh.
The fourth-placed visitors put Saints under pressure in the closing stages, but the home side defended well to register another win.
TNS: Harrison, Spender, Hudson, Astles, Marriott (Harrington), Smith, Holland, Routledge, Robles (Mullan), Draper (Ebbe), Cieslewicz. Subs not used: Clark, Boateng, Rees, Williams.