Lawrie Wilson found the bottom right-hand corner with 18 minutes to go to secure the points for Westley's side.
Westley said: "I'm delighted for all the lads because it was a real team effort.
"We've put ourselves in a great position to get promoted, but there's obviously still a long way to go. We've got another two tough matches to play before we can even think about making sure of our play-off place.
"I knew it was going to be a really tough game against Port Vale because they were trying to get in the play-offs as well, but I thought we deserved the victory and we could have won by more.
"But it's fair to say we rode our luck at times and we have to hang on because they threw everything at us. But the players showed enormous character to get the victory. It was a good goal from Lawrie Wilson, he's scored a few for us this season, but probably none as important as that."
Source: PA
Source: PA