Pablo Ibanez headed in his first goal since a summer move from Atletico Madrid on 12 minutes, and substitute Chris Wood, the New Zealand striker, slotting in a second during stoppage time.
Mantom also caught the eye, the 18-year-old England youth international having come back from a spell on loan in Iceland with Haukar ready to challenge for a first-team place.
"A couple of the Academy boys came in and made a massive contribution, Sam Mantom was outstanding in his first game for the club," said Baggies first team coach Appleton, who himself had played as a youngster in the League Cup for Manchester United in 1996.
"He is a good footballer and of all the boys we have had out of the Academy, he was one of those we knew would mature later.
"He used to get knocked off the ball a lot in youth team games, but always showed that ability.
"It did him the world of good when he went away to Iceland in the summer and played for two months over there.
"It is probably a bit early for him in the Premier League right away, but it is a long old season and there will be injuries."