This means that Linlithgow remain top of the table on 62 points from 26 games, two points clear of second placed Penicuik who have played a match fewer.
Third placed Tranent Juniors are also still in title contention, having accumulated 59 points from 25 fixtures.
Rose manager Gordon Herd said: “The Penicuik result was a big result for us, we didn’t expect that.
"Liam Allison, who is actually on loan to Blackburn from Linlithgow, has actually done us a big favour.
"He’s scored the equaliser and he’s set up the winner as well.
"There are going to be a lot of twists and turns in this league before the end of the season.
"We just need to get our house in order because we’ve fallen away the last couple of games.
"And it can happen after you get a defeat, confidence can go. So we just need to pick ourselves up, refocus and we go again.”
Linlithgow have two more League Cup Section J games coming up, away to Luncarty this Saturday and at Blackburn next Wednesday, March 16.
Their next league game is at Hill of Beath Hawthorn on Saturday, March 19.