Mark Stowe’s early penalty – awarded after a foul on Lewis Payne – put Rose ahead in Perthshire before Ben Scarborough levelled for the hosts before half-time. And the visitors went on to earn the point which booked a home tie against Lothian Thistle Hutchison Vale in the next round on Saturday, April 30.
"It was a potential banana skin for us,” said Rose boss Gordon Herd. “It was a 6.30 kick-off so guys were having to leave work very early.
"The League Cup sections have thrown up some funny results so it was good to get the point we needed and we’re into the next round, that’s the main thing. The performance level wasn’t the greatest.
"We could have won the game but to be fair to Luncarty they pressed us near the end looking for that winner. They’ve had a couple of balls across the box, they’ve had a shot over the bar.
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"Linlithgow have been starved of cup success for eight or nine years so the aim is to bring a trophy home.
"We’ve got a big month ahead. We want to be in cup finals and the final shake-up for the league.”
Linlithgow will resume their East of Scotland Premier Division campaign at home to Sauchie this Saturday.
With six league fixtures remaining, Rose go into the match third in the table with 62 points, behind leaders Tranent Juniors and second placed Penicuik Athletic who are both on 66 points.
Herd’s team still have to play Tranent home and away and Penicuik away before the season ends, so their title dreams are still very much alive but beating Sauchie this weekend looks essential if they are to go on and fulfil that aim.
"Sauchie will be a hard game,” Herd said. “The boys need to be up for it.
"Every game’s a cup final in the league.
"If we turn up and play how we can play we should take the three points but Sauchie will come and make it tricky for us, they’ve been on a good run of form.
"The league title is in Penicuik’s hands. If they win all their games they win the league.
"We need Penicuik to drop a point or two for it to be back in our own hands.
"It’s up to Penicuik. They’re favourites at the moment because we’ve still to play Tranent twice. It’s Penicuik’s to lose.
"We gave ourselves a great chance by going on a winning run but we’ve slipped up in the last month or so.
"We just need to take it one game at a time and see where it goes. That’s the message we’re giving to the boys.
"We can’t control what goes on around us but we can control what we do.”
With the big games coming thick and fast, Rose also have a home game against Lowland League Stirling University in the East of Scotland Cup semi-finals next Tuesday night.