Chasing their seventh straight win, Rose led at the break through Keiran McGachie’s header midway through the opening period at New Dundas Park.
McGachie headed a second just after the hour, but the visitors, who had already shown they carried a threat, pulled one back when Jamie Penker fired past Rose keeper Michael Andrews.
However, substitute Kieran Hall’s finish four minutes from time secured the win and kept Rose a point ahead of Rangers B at the top of the table.
Rose boss Robbie Horn admitted his side can play better but said the priority was getting the victory.
He said: “We didn’t play anywhere as near as well as we can, but we got the three points and that’s the most important thing.
“Michael had to make a few saves in the game, to be honest, but we missed chances ourselves and had two cleared off the line.
“I don't think we’ve played as well as we can yet this season, which is frustrating, but at the same time, if you’re winning, you can’t complain too much.
“We’ve been unsettled with Covid and have had people away at different points as well. It’s just the way it is this season. We’ve been in the pandemic for some time and boys are going to have weddings or stag dos or whatever else.
“Injuries as well will be a big factor. There are guys who haven’ t played for a long period of time and already we’ ve played 10 league games by the end of August.
“Other teams will have the same situation and it’ s whoever deals with that best that is going to come out on top.”
Next up for Rose on Saturday is a home match against Horn’s old club Berwick Rangers, currently fourth in the table and 5-1 winners over Cumbernauld Colts on Saturday.
Horn said: “It will be a really difficult game. They’re obviously playing well and have spent a bit of money over the summer and brought in some experienced players, so I’m expecting a really tough challenge.
“I expect Berwick to be up there come the end of the season with the players they’ve brought in, so it’s a big test and we need to be ready.”