Penicuik drew first blood in both sides’ last game of the season after seven minutes.
Keith Lough’s corner was fizzed across goal and Young powered a header into the net past Bonnyrigg replacement goalkeeper Dylan Rooney, who came into the squad in place of number one Michael Andrews, who was on holiday.
Rose gradually came into the final, enjoying most of the possession in the final third, but they struggled to carve out many chances.
Keiran McGachie was on the end of their best opening after half an hour but he found himself offside as he shot wide.
Rose, who ended the season 32 points ahead of Penicuik in the league, finally got level after 40 minutes. Striker Wayne McIntosh chipped a perfect ball into the box which Nelson met to glance a header past keeper Youssef Bejaoui.
The equaliser didn’t knock Penicuik out their stride, however, as McCallum pounced in the final minute of the half and curled an exquisite left-foot strike into the top corner past Rooney.
Rose had a penalty appeal waved away on 57 minutes as Bejaoui challenged McGachie in the box, but referee Scott Miller wasn’t interested.
Bonnyrigg were struggling to break Penicuik down, who were quite happy to sit back and defend, with player manager Craig Meikle leading by example at the heart of their defence.
The crucial third goal to kill of Rose’s challenge arrived after 73 minutes. Rooney failed to deal with a ball across the face of his goal with the ball landing nicely for Aaron Somerville at the back post, who cut the ball back inside the area for the onrushing Patterson to slide into an empty net.
Bonnyrigg Rose: Rooney, Archibald, Donaldson, Stewart, Moyes, Hoskins, Gray (Kidd), Turner (McLaren),
McGachie (Tobin), Nelson, McIntosh.
Penicuik Athletic: Bejaoui, Devlin, McDermott, Meikle, Young, Lister (Patterson), Barr, Janczyk, McCallum, Somerville, Lough.