The Norwich City striker led the team from behind, setting up Niall McGinn's equaliser before scoring the winner two minutes from full time.
The manager told Sky Sports News: "Kyle came up trumps, giving a big performance for the 90 minutes. Kyle knows how important he is to us.
"We've not had him available to us enough, but when you see him like tonight, focused and energised, he gives a lot to the team.
It enhances my belief that we can compete in this group. It's always difficult to not get carried away with one result, but that's all it is. Hopefully we can carry this on throughout the campaign."
The victory is Northern Ireland's first away from home in four years.