The highly-rated youngster found the net from close range in the 75th minute, sending the crowd of more than 42,000, largely made up of Liverpool supporters, into celebration as the Reds secured a second successive win on their United States tour.
The result followed Liverpool's entertaining 4-2 victory over Sunderland in Nashville, giving Iraola another positive outing as he continues to shape his side after replacing the departed Arne Slot.
Ngumoha's goal was enough to settle a competitive contest against a Wrexham team that has continued its remarkable rise under owners Ryan Reynolds and Rob McElhenney. Phil Parkinson's side arrived in New York full of confidence after impressive pre-season victories over Manchester United and Leeds.
Liverpool were again without several key players. Defender Joe Gomez missed the match after suffering an injury against Sunderland, while new signing Jeremy Jacquet was also unavailable. FIFA World Cup stars Ryan Gravenberch, Florian Wirtz and Alexander Isak were given more time to recover following their international commitments.
Before the match, Iraola said Gravenberch, Wirtz and Isak could all return for Liverpool's final game of their US tour against Leeds at Soldier Field in Chicago on Sunday.
Although it was only a pre-season fixture, Liverpool showed encouraging signs once again under their new manager. The Reds controlled large periods of the match, while Ngumoha's composed finish highlighted the exciting talent emerging from the club's academy as preparations for the new season continue.
Jack Grealish has dismissed suggestions that he was dropped from Manchester City's pre-season tour, insisting he is still recovering from injury rather than being left out by head coach Enzo Maresca.
Chelsea have completed the signing of defender Maxence Lacroix from Crystal Palace in a deal reported to be worth 52 million pounds.
Newcastle United have decided to amicably part ways with manager Eddie Howe just a few weeks ahead of the upcoming 2026/27 campaign.
Tottenham manager Roberto De Zerbi has made it clear he wants Lucas Bergvall to remain at the club, but insists no player can expect an automatic place in his starting line-up.
