Swindon overcame a depleted MK Dons, who were reduced to 10 men for the fourth consecutive game.
Suspension and injury meant manager Karl Robinson could not fill the bench, and their personnel problems worsened when Dean Lewington was sent off for lashing out at Simon Ferry.
The hosts went ahead just before half-time through Matt Ritchie's cross-shot, which snuck in at the back post.
Darren Potter came close to equalising late on but Wes Foderingham saved well.
MK Dons see red
v Cheltenham Town (League Cup)
Dons goalkeeper David Martin kept his side in the game in the early stages, saving from Raffaele De Vita's bullet strike and twice from Aden Flint.
Lewington caught Ferry with his arm and received a straight red on 39 minutes - a decision which angered an already frustrated Robinson.
Swindon instantly capitalised on their numerical advantage as Ritchie's ball drifted past Martin, although striker James Collins claimed to get the last touch.
VIEWS FROM THE DRESSING ROOM
Swindon Town manager Paolo Di Canio told BBC Wiltshire:
"It probably wasn't our best game but in the first half we played our football (but) the second half I didn't completely enjoy because we played at a very low tempo.
"We should have won with a (more) comfortable result.
"Before the sending-off we were the only team who should win the game.
"Since that moment we didn't play the same football."
Swindon Town 01 Foderingham 03 McEveley 04 Flint 05 Devera Booked 08 Ferry Booked 10 Ritchie 12 McCormack 18 Miller 09 Collins (Storey - 87' ) 16 Williams 23 De Vita (Navarro - 73' ) Substitutes 30 Bedwell 15 Thompson 32 Smith 06 Navarro 07 Rooney 13 Risser 20 Storey Milton Keynes Dons 01 Martin 02 Otsemobor 03 Lewington Dismissed 05 MacKenzie Booked 12 Chicksen (Ibehre - 75' ) 08 Potter 17 Powell 23 O'Shea (Williams - 42' ) 26 Chadwick 09 Bowditch 14 Lowe (MacDonald - 64' ) Substitutes 16 McLoughlin 27 Spence 06 Williams 21 Ali 10 MacDonald 19 Ibehre