McCoy popped up from close range with 10 minutes left to deny Ross Turnbull a clean sheet on his United debut, the former Barnsley ‘keeper having joined the Elland Road club earlier on Wednesday.
After a delayed kick-off because of crowd congestion – there were more than 2,300 Leeds fans in a crowd of 4,348 – Leeds took their time to get into the game before summer signing Lee Erwin tested home ‘keeper Scott Flinders.
Flinders also denied Steve Morison, who came into Uwe Rosler’s side after Chris Wood was injured in the warm-up, but he could do nothing about Sam Byram’s 35th-minute opener.
The goal came thanks to hard work down the left from Alex Mowatt, who made some space and put over a perfect deep cross that Byram headed home at the far post.
United stayed in control after half-time, with Byram firing wide and Gaetano Berardi testing sub goalie Michael Ingham, who also made a smart save to deny Leeds trialist Adam Drury.
Busy Ingham made his best save 15 minutes from time when Morison’s volley was acrobatically tipped over the bar by the 35-year-old.
And Leeds were made to pay for their wastefulness in front of goal with 80 minutes on the clock, Anthony Straker getting over a cross which McCoy tapped home at the far post.
Leeds also had an XI in action against Tadcaster Albion, where goals from Mirco Antenucci, Billy Sharp and Souleymane Doukara were enough to secure a 3-0 win.