A superb Matty Williams strike after 37 minutes put the Saints in front as they dominated first-half proceedings in south Wales.
Richie Partridge did the spadework before passing to Williams who took the ball round Paul Cochlin before crashing an 18-yarder past keeper Wyn Walters for his tenth goal of the league campaign.
And TNS went close to increasing their lead after the break on a couple of occasions after the break.
Tommy Holmes headed over the bar from a dinked Partridge cross and Walters palmed away a header from Craig Jones with Williams just unable to connect with the rebound.
The Eagles rarely threatened as an attacking force but, with 11 minutes left, Phil Baker brought down Trundle on the edge of the box and the former Swansea man made no mistake from the spot.
Only a last-ditch intervention from Tommy Holmes prevented Chad Bond from immediately adding another, but Aeron Edwards almost grabbed a winner three minutes from time, denied by Walters after being put clear by sub Alex Darlington.
Photo: Matty Williams crashed home the Saints' goal.