© Dave Thompson / PA Photos
The visitors attacked in numbers early on and Blackburn needed a brave block from Grant Hanley to stop Ross McCormack putting Leeds ahead.
Michael Appleton's side came into the match before the break but were unable to stop the first half ending in a stalemate.
McCormarck had a gilt-edged chance to put Leeds ahead just after the interval but could only find the side netting from close range.
Both sides went for a winner in a frantic finish but Rhodes and Varney both missed clear openings in the closing stages as the match ended goalless.