But Simon Cox pulled one back for Swindon before Barry Corr levelled with four minutes remaining.
The result left Leicester a point off leaders Scunthorpe, who were 2-1 winners at Bristol Rovers on Friday.
Carlisle ended a run of 12 games without a win with a 3-1 home victory against Brighton, who host Town on Saturday.
A double by Bradford old boy Marc Bridge-Wilkinson and Cleveland Taylor’s strike put the hosts 3-0 up before Matt Richards netted a consolation for Brighton, who are 15th, a place and a point behind Town.