Adam Smith put the Minstermen in front 24 minutes in, only for Luciano Becchio to equalise 15 minutes later.
Youngster Mike Whitwell put Leeds in front five minutes into the second half and Andy Milne looked to have wrapped up the game for the visitors when he struck eight minutes from time.
But Alex Lawless pulled a goal back in the 90th minute and an unnamed City trialist denied Leeds victory with a dramatic late leveller.
Leeds manager Simon Grayson named two different XIs for each half, with goalkeeper Shane Higgs and right-back Jason Crowe making their first appearances for the club during the opening 45 minutes. Jermaine Beckford also began the match.
Forward Enoch Showunmi played the second 45 minutes after seven months on the sidelines with injury.