Marcelo Bielsa' s Whites fell behind in the 71st minute as Connor McBride's free-kick deflected past 'keeper Illan Meslier but Pascal Struijk slotted home a deflected equaliser nine minutes from time.
Summer signing from Barcelona Junior Firpo was handed his Whites debut and Lee Sobot hands out the scores from the displays at Ewood Park.
United are back in action on Friday night at Fleetwood Town, after which Leeds will take on Firpo's former side Real Betis at Loughborough University on Saturday lunch time.
The Whites then play Ajax in Amsterdam next Wednesday ahead of the new Premier League season which will begin with a clash against arch rivals Manchester United on Saturday, August 14.
United are back in action on Friday night at Fleetwood Town, after which Leeds will take on Firpo's former side Real Betis at Loughborough University on Saturday lunch time.