Leeds made a dream start, Robert Snodgrass scoring in the second minute, aided by a goalkeeping error by Alex Smithies. When Smithies somehow failed to hold Sam Vokes' tame shot, Snodgrass drove the ball into the centre of the goal from seven yards.
Town's top scorer Rhodes powered a shot against a post soon afterwards and shortly before half-time Snodgrass went close to scoring again when his clever overhead effort shaved the upright.
Huddersfield enjoyed ample possession and Lee Novak equalised in the 48th minute. Leeds failed to clear a corner and Nathan Clarke's shot was deflected to Novak who headed home from inside the six-yard box.
Leeds regained the lead after 67 minutes. Beckford leapt to challenge Smithies for a long ball which broke for substitute Max Gradel to fire into the bottom corner from a narrow angle.
Town hit back again in the 78th minute when Lee Peltier and Gary Roberts combined on the right, Roberts crossed and Rhodes headed home the leveller.