Fraserburgh were cruising 3-0 up by the break but they had a nervy final 25 minutes after Dalbeattie scored twice in three minutes around the hour mark.
Fraserburgh assistant manager James Duthie said: “We were very comfortable in the first half having scored three goals and it probably could have been more but in the second half we just didn’t start and we were pretty poor. Dalbeattie Star were a lot better after the break.
“In the first half we could have scored any number of goals and the second 45 minutes were a total turn-around as we just didn’t do the things we were doing so well in the early part of the game at all.
“Whether the players got complacent or not I don’t know but we had done our preparation well and we knew all about them. After half-time they won every second ball and deserved to score their two goals but we hung on to reach the next round.”
Broch were 3-0 up at the break thanks to a Graham Johnston penalty and a Marc Lawrence double but goals in the 60th and 63rd minute from Star’s Lewis Sloan and James McHarrie set up a nervy finish.
Scottish Cup highlights: Fraserburgh 3-2 Dalbeattie Star