The 25-year-old's form was good enough to attract bids from Middlesbrough back in August but a knee ligament injury and then a knee cartilage operation ensured frustrating spells on the sidelines.
The former Ayr winger returned to action earlier this month after 11 weeks out and was instrumental in United securing consecutive home wins to move into sixth in the table. Conway's return to form will be welcomed by manager Peter Houston, whose team have struggled to land the full three points in a run which has seen them draw six of their last seven games.
He said: "It's been a really stop-start season for me. It started all right and then kind of went downhill from there, really. But that's it now, I'm back playing, and I've just been picking up a couple of wee niggles here and there.
"Hopefully I can finish the season how I did last season. After Christmas I felt really good and kicked on. I'm looking to do that now.
"I know what I can do and I just want to kick on, and something I need to do is add goals to my game as well. I did that on Sunday and hopefully I can go on from there."