Defender Matthew Langston's 39th minute header from a Gareth Gwillim corner stunned the Whites and earned non-league Histon a home tie with Swansea in the next round.
On a water-logged pitch at a rain-lashed Glass World Stadium Histon had hardly threatened the Leeds goal up until then as all their long ball deliveries had been well marshalled by Lubomir Michalik.
Patrick Ada nearly conceded an own goal and Luciano Becchio should have done better from an excellent Robert Snodgrass cross from the wing as Leeds attempted to pass the ball in awkward conditions.
Michalik himself twice came within inches of equalising for Leeds, first seeing his shot bounce back off a post with the keeper well beaten and then a fierce drive was headed off the line by sub Antonio Murray late on.
But the home side held firm as Leeds were left shattered by the defeat, their first ever against a non-league outfit.
Histon: Naisbitt 6, Oyebanjo 6, Langston 8, Ada 7, Gwillim 7, Barker 6 (Murray 50 7), Mitchell-King 6, Simpson 6, Knight-Percival 6, Wright 6, Midson 6.
Subs (not used): Welch, Pope, Okay, Kennedy, Andrews, Reeves.
Leeds United: Lucas 6, Richardson 6, Marques 6, Michalik 7, Sheehan 6, Delph 6, Douglas 6, Snodgrass 7, Robinson 5 (Showunmi 52 6), Becchio 6, Hughes 5 (Howson 59 5).
Subs (not used): Ankergren, Prutton, Kilkenny, Parker, Telfer.
Referee: Neil Swarbrick (Lancashire) 7/10.
Match Rating 3/5
Attendance: 4,500.