But more than 36,000 fans saw Jordan Rhodes' header 12 minutes from time earn a point for the Terriers after United had threatened to extend their lead at the top of League One to nine points.
And the visitors could have won it in the dying moments but a pile-driving free-kick from Antony Pilkington hammered against the crossbar and bounced down to a grateful Casper Ankergren in the Leeds goal.
Leeds went ahead after just two minutes through Snodgrass who was on hand to prod home from close range after Alex Smithies could not hang on to Sam Vokes shot.
The Terriers came within a whisker of an immediate response but Rhodes' effort struck an upright while Gary Roberts screwed a shot wide when well-placed moments later.
United came close to extending their lead again on 14 minutes. Jermaine Beckford whipped in a cross from the right and Vokes glanced a header just wide of the upright.
Huddersfield continued to create problems for the Leeds defence and Ankergren had to be alert to cut out a low cross from Pilkington.
Huddersfield did see more of the ball as the game headed towards half-time, but United looked solid at the back, and looked to move the ball quickly in reply.
Beckford's movement was first class and it was after more good work by the striker that Snodgrass hit the base of the post.
The visitors did enjoy a spell of pressure during the final moments of the first half, though, Roberts again wasted a decent opportunity while Rhodes should also have done better when the ball broke to him just yards out but Ankergren was able to save.
The visitors got back level two minutes into the second half when United failed to clear a cross and Lee Novak headed home inside the six-yard box.
United almost restored the advantage within two minutes, Beckford twice being denied by some desperate defending.
Neil Kilkenny threaded a ball through to Beckford, but Smithies reacted quickly to smother at the striker's feet.
A spectacular overhead effort from Antony Kay nearly put the Terriers ahead but his super strike was straight at Ankergren who immediately launched the ball upfield.
Beckford challenged Smithies in the air and the ball broke to substitute Gradel who rifled the ball into the bottom corner.
Town pressed for the equaliser and Ankergren had to be alert to deny the visitors, bravely diving at Novak's feet to push the ball out for a corner.
However, they were not to be denied and with the Leeds defence vainly appealing for offside, Rhodes' header found its way into the bottom corner with just 12 minutes remaining.