The 21-year-old striker netted just before half-time in a relatively calm game for the touring Premier League team, who gave starting roles to two of their new signings
The Premier League side dominated proceedings, with Delfouneso coming close on a number of occasions, as well as a long range effort from Ciaran Clarke and a couple of chances for new midfielder Brett Holman.
A host of substitutions in the second half slowed the game down, and the Union came close to equalising when Josue Martinez struck a shot wide after bursting past Richard Dunne, but Villa looked comfortable for much of the game.
Lambert named an experienced side for the clash on the east coast of America, with Darren Bent named captain for the friendly. There were spaces in the starting XI for new signings Holman and Karim El Ahmadi, as well as Brad Guzan, who was re-signed by Lambert after temporarily leaving the club following the expiration of his contract.
Villa almost took the lead in the opening minutes after right-back Matt Lowton's cross was turned goal-wards by Holman, but Union keeper Zac MacMath made a good save to deny the Australian his second goal of the pre-season.
MacMath was in action again 10 minutes later, denying Delfouneso from close range as he bore down on goal.
Moments later, Union defender Amobi Okugo was booked for a challenge on Bent just outside the box, and from the resulting free-kick the England striker shot straight at MacMath, who was having a busy night in the opening 20 minutes.
Villa were on top throughout the first half, with Guzan barely tested. Clark came close for the visitors, letting fly from 35 yards, but he saw his effort fly just over the bar.
And after 43 minutes Lambert's side took the lead. Stephen Warnock was the creator, sliding a ball through to Delfouneso, who curled the ball into the far corner from the edge of the box to give the Villans a half-time lead.
The English side made a raft of substitutions after half-time, with nine new players joining the action in the first 20 minutes after the break. The changes weren't conducive for great football in the second half, but were to be expected in a pre-season game played out in humid conditions.
With just over 15 minutes to go, Union had their best chance of the match as Josue Martinez sped past Richard Dunne down the left, but his angled shot went just wide of the post.
Villa played out the remaining minutes with relative ease in front of an announced crowd of over 17,000 fans, with a free-kick struck into the wall the only point of danger and N'Zogbia forcing a save in stoppage time, but in truth it wasn't too much of a test for the Premier League team.