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.
1. Illan Meslier
7 - A strong return from United's no 1 'keeper who was alert throughout and had no chance with Connor McBride's deflected free-kick, but for which he would have kept a deserved clean sheet. Picture by Richard Sellers/PA Wire.
2. Jamie Shackleton
7 - A decent shift at right-back from the 21-year-old who was involved in one particularly fine move in the first half that ended with Raphinha scuffing his shot. Energetic and got forward when he could. Photo by Lewis Storey/Getty Images.
3. Pascal Struijk
8 - Solid at centre-back and kept a cool head to slot home the equaliser, albeit via a deflection. Denied a headed goal earlier via a strong save and made some lovely diagonal passes. Still only 21 and rapidly improving. Picture by Richard Sellers/PA Wire.
4. Diego Llorente
7 - Ran Struijk close with his performance in the first-half but was subbed at the break for Luke Ayling. Produced a superb tackle on Adam Armstrong to force a corner and snuff out a golden Rovers opening. Photo by LEE SMITH/POOL/AFP via Getty Images.