Ireland fly-half Jonny Sexton also kicked eight points for Leinster as the picked up their first win on the road this season.
And Strauss said: "We have found it hard coming here over the last few years and we made some mistakes, but we're pleased to get the win and our fist victory on the road.
"Connacht are a really good side and they put a lot of pressure on us. I don't think our last try was a fair reflection on them, but it was important that we kept up our recent good form.
"We have struggled a bit on the road this year, so it was an important win for us."