The Reds went ahead after 11 minutes when Will Keane's shot from close range was blocked and the ball ran to trialist Souleymane Mamam who scored, via a deflection, from an angle.
Playing their usual brand of stylish football, Warren Joyce's side dominated most of the first half with Danny Drinkwater and Larnell Cole registering efforts before a 25-yard piledriver from Jesse Lingard grazed the bar.
Craig Williams and Lee Surman spurned identical glaring opportunities to haul Llanelli back onto level terms and the visitors had to battle for supremacy after the break.
Ravel Morrison entered the fray and looked sharp, embarking on a couple of his trademark solo slaloms through the defence. One such run led to a cracking drive that tested Ashley Morris. Paul Pogba then brought the very best out of Morris with a 30-yard drive that arrowed goalwards before being diverted over the top by the keeper's fingertips.
With seven minutes left, United doubled their lead and sealed a deserved victory in a match they clearly edged. Pogba was fouled inside the box but saw his spot-kick saved by substitute keeper Craig Richards. The ball squirmed back to Pogba who followed up to tap home.
United: Amos; Cole (Leao 85), Vermijl, Fornasier, Fryers; Pogba, Mamam (Morrison 58), Drinkwater, Lingard, Petrucci (Giverin 58); W.Keane (Cofie 46).