Charlie Austin had given the home side a first-half lead when he was played clear by McGovern and finished calmly.
Wednesday striker Clinton Morrison equalised in the 30th minute to send the sides in at half-time on level terms, but it was McGovern who sealed the win for Swindon when he stabbed in a long throw.
You can read a report of all the action by following the link below.
Welcome to the Yorkshire Post's exciting match-day service, called Match Centre. Here you will find minute-by-minute updates, stats and team formations. Plus reports from every game in England, from the Premier League down to the Blue Square Premier.
Simply select your game from the pull down menu, then click on the 'i' information button on the right of the fixture and it will give you access to everything you need to know about your team.
So if you can't make it to a game, head for the Match Centre and we will give you the best seat in the house. Click the link below.
For the latest team news, score and commentary from your team check out our new Match Centre
For full reports read Monday's Yorkshire Post.