In-form Michael O’Connor hit the bar as Vale were denied by a fantastic performance by visiting keeper Wes Foderingham.
Rob Page unsurprisingly brought in Ryan McGivern for Ryan Inniss but Vale were otherwise unchanged. But the home side started slowly and Swindon took an eighth minute lead through Branco although Vale may argue that keeper Chris Neal was impeded.
For the majority of the rest of the first-half Vale forced the pace but just could not get an equaliser despite chances for Moore, Marshall and Williamson.
Vale continued to press in the second-half and were desperately unlucky not to equalise when Michael O’Connor’s free-kick hit the crossbar.
The Valiants continued to press and Rob Page brought on Daniel for the injured Moore and Louis Dodds for Tom Pope who had had a quiet game. Vale continued to attack after the changes and Ben Williamson was sent clear but the chance was wasted. Then sub Dodds forced a great save from Foderingham.
The home side continued to try and force an equaliser but somehow the ball would just not go into the net and Vale’s play-off hopes suffered another blow.
Vale: Neal, Veseli, McGivern, Robertson, Dickinson, Marshall, Brown, O’Connor, Moore (Daniel), Williamson, Pope (Dodds)
Subs: Johnson, Birchall, Yates, Duffy, Lloyd