County were beaten on Tuesday night by Salford City and yesterday's victory over Leamington was by no means easy.
Oswell put Stockport in front but the hosts equalised through Robert Thompson-Brown to level the scores going into half-time.
It took until late in the match for the drama to really unfold. Liam Canavan edged Leamington in front after 82 minutes but four minutes later Oswell equalised and then in the 90th minute he struck again for his hat-trick and the match winner.
"It was a very tough game," Oswell told the club's website. "It's not one of those that you come in and you're absolutely happy with. When we went 1-0 up we probably thought it was going to be quite comfortable, but we let them get back into it.
"In the end we're probably lucky to get the win but they're the games you need to win in the season. Because we lost on Tuesday, we needed these three points.
And on his hat-trick, taking his tally to six goals in four games, Oswell said: "They were three great deliveries and without that you can't score so a lot goes down to the team.
"We've been working on that in training, putting balls into the right areas. I know where it's going to go so that's where I make my run."