Marco Silvestri had to be alert in the opening minutes as Harrogate dominated the early possession, but it was Leeds who had the first real chance when Liam Cooper's header was parried by Peter Crook, before Chris Wood rifled the rebound into the side-netting.
Jordan Thewlis made a quick break for the hosts as they continued to create opportunities, but Silvestri was able to pull off a diving save to stop the ball sneaking into the bottom corner.
It was the home side that broke the deadlock with just over half-an-hour gone, though, as Cecil Nyoni deflected a free kick past Silvestri from close range.
Crook was kept busy in the final stages of the first half as Leeds pushed for an equaliser, but Mirco Antenucci was denied twice by the keeper in the space of two minutes.
Ross Killock came close to putting the visiting side in front for the first time just after the hour mark as the defender tried to poke the ball in from a corner, but it ended up going behind.
Both sides had chances to seal the win from free kicks late on as Charlie Taylor fired just over for Leeds moments after Thewlis had struck over down the other end for Harrogate, ensuring that the sides finished level.