Striker Trundle, on loan from Bristol City and making his full Leeds debut, cashed in on slack defending to put his side ahead on the hour in Saturday's League One clash at the Withdean Stadium.
Highly-rated midfielder Delph settled the issue eight minutes from time with an unstoppable left-footed shot following a swift counter attack.
Substitute Malcolm Christie should have made it more convincing for Leeds but missed an open goal late on.
Referee Pat Miller had earlier awarded Leeds a 10th-minute penalty after penalising Adam El-Abd for a push on Luciano Becchio. However, young goalkeeper John Sullivan parried Becchio's spot kick which was struck down the middle and the ball was scrambled to safety.
Striker Stuart Fleetwood, on loan from Charlton, should have given Brighton the lead when clean through with only Casper Ankergren to beat but his tame shot was easily saved by the Leeds goalkeeper.