Striker Jermaine Beckford scored twice for Leeds as they beat boss Dennis Wise's former club. Beckford fired a penalty high into net after Hasney Aljofree was adjudged to have handled David Prutton's cross.
Simon Cox crossed for Lee Peacock to equalise from close range less than a minute after the interval.
But Beckford drove in the winner after being found by Tresor Kandol's pass, before Cox netted late on but had his effort ruled out for a handball.
Leeds: Ankergren, Richardson, Marques, Heath, Clapham, Prutton, Howson, Hughes, Carole (Kishishev 61), Kandol (De Vries 83), Beckford (Constantine 90).
Subs Not Used: Huntington, Thompson.
Booked: Beckford.
Goals: Beckford 32 pen, 56.
Swindon: Brezovan, Comminges, Ifil, Aljofree, Zaaboub, Roberts (McGovern 83), Easton (Corr 73), Pook, Peacock, Paynter, Cox.
Subs Not Used: Nicholas, Tozer, Scott.
Booked: Aljofree, Comminges, Roberts, Easton, Pook, Cox, Paynter.
Goals: Peacock 47.
Att: 27,990
Ref: Lee Mason (Lancashire).
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