Derby 2 Sheffield United 0
By Andy Clarke
Last Updated: 01/01/70 1:00am
Tudgay struck with a powerful header to give Derby the lead on 70 minutes, before substitute McLeod sealed the win in injury time to move the Rams above local rivals Nottingham Forest, who drop into the bottom three.
The Blades could have moved above West Brom into second place had they won, and they made the brightest start, with Nick Montgomery and Paul Shaw both going close.
However, it was Derby who wasted a glorious chance on 10 minutes, when Marco Reich could only scuff Candido Costa's cross straight at Paddy Kenny.
Mark Rankine then could have scored for United from Alan Wright's superb cross, but saw his bullet header well saved by Lee Grant.
Derby felt they should have had a penalty on 55 minutes when Leon Osman's run was ended by Robert Page's challenge, but referee David Crick waved away their appeals.
But the breakthrough came 15 minutes later when Reich's centre was firmly headed beyond Kenny by Tudgay.
United boss Neil Warnock threw on Paul Peschisolido and switched to a three-man attack as the visitors went in search of an equaliser.
But Derby's defence held firm and the home side wrapped up the points in the dying seconds when Kenny failed with a routine clearance and McLeod slotted in.