Cook's 43rd-minute strike was enough to seal victory for the Americans, who were playing their final game before head coach Vlatko Andonovski picks his World Cup squad.
The defender's long-range effort came with a slice of good fortune, Ireland goalkeeper Courtney Brosnan making a hash of her attempt to gather the ball and palming it into her own net.
The US win was the second time in three days that the USA had beaten Ireland.
The 2019 World Cup winners scored a 2-0 victory over the Irish women last weekend in a game overshadowed by an injury to star forward Mallory Swanson.
The Americans have one more game before opening the defence of their World Cup title in Auckland against Vietnam on July 22nd.
US Soccer announced earlier Tuesday that Andonovski's side would play Wales in a friendly in San Jose, California on July 9th.
The send-off fixture will be the first time the US women have faced Wales at international level.
"We're really looking forward to having an exciting, productive camp and playing one last match to fine-tune some things before we leave for New Zealand," Andonovski said.
