Swindon began the double-header with a comfortable 5-2 win at home on Saturday.
Shaun Thompson had actually given the Bees an early lead at the Link Centre but Max Birbraer ensured parity was restored by the end of the first period.
Again, it was Bracknell who struck first after the restart when Scott Spearing hit the back of the net but again Birbraer was the man to respond for Swindon as the second period ended level.
It was one-way traffic in the third period as Floyd Taylor put the hosts ahead for the first time on the night before further strikes from player-coach Aaron Nell and Luc Johnson completed the Cats’ win.
Sam Bullas then fired an overtime winner for Swindon as they completed a perfect weekend with a 5-4 victory in Sunday’s away fixture.
The first period in Bracknell failed to produce a goal but the two teams traded four strikes in the second, with Birbraer and Edgars Bebris on target for Swindon as Thompson and Josh Smith replied for the hosts.
Spearing and Aidan Doughty twice gave Bracknell the initiative in the third period but Sam Jones and then Chris Jones levelled matters to send the contest to overtime.