Omer Riza, pulled down in the 49th minute, and Richard Garcia, fouled 60 seconds later, were the players who won the spot kicks - both tucked past former Hammers custodian Ian Feuer.
The second foul led to a sending off, but West Ham were unable to exploit the extra man by adding toi the score.
Roger Cross says of the opening reserve fixture of the season:
"It was great to get off to a winning start and I was very pleased with the performance.
"We were very sound defensively - I was particularly pleased with Steve Potts and Ragnvald Soma.
"There was good passing, movement, and we were excellent going forward.
"Omer Riza was desperately unlucky not to score in what was a competitive match from start to finish."
The game saw the return to action of Scott Minto.
There were bookings for Omer Riza, Glen Johnson, and Richard Garcia.
Forrest, Johnson, Minto, Cascione [Ferrante 70], Potts, Soma, Newton, Britton [Eastwood 77], Garcia, Riza, Courtois.
Subs unused: Clark, Uddin.