Cantlay birdied the final three holes as he and Wyndham Clark snatched a 1-up fourballs victory over McIlroy and Matthew Fitzpatrick to cut Europe's lead to 10.5-5.5 heading into the last day.
The USA will be hoping to use the momentum to pull off the biggest comeback in Ryder Cup history and lift the trophy on European soil for the first time in 30 years.
"Matt and I played well. Obviously they had a great finish and Patrick made three great putts at the end to seal the deal, so hats off to them," said McIlroy, who had won his previous three matches in Rome.
"They played a great match, and... a few scenes there on 18 and just fuel for the fire tomorrow."
Europe had led by seven points after Saturday morning's foursomes, but remain in a strong position to regain the trophy after their record 19-9 thrashing at Whistling Straits two years ago.
