A Chris Templeman goal gave Montrose an important win and extended their lead at the top of the table to four points.
A largely disappointing encounter was short on goalmouth action and there never seemed any chance of a repeat of the eight goals witnessed at Links Park at the end of last year.
Montrose boss Stewart Petrie said: “It’s a difficult venue to come to. It’s not going to decide who goes up but it is a big three points.
“If we had lost Peterhead would have been clear with games in hand and they are a big strong side with some good footballers.
“I thought we had the better of the first half without creating many chances and Peterhead had the better of the second without really troubling us.
“It was a tight game throughout and one goal looked like winning it.”
Montrose headed north for the eagerly-awaited clash at Balmoor with their hosts in second place in the table, a point behind but with two matches in hand.
With the Fleming brothers in each goal, it was the visitors’ Allan who was first in action, a flashing cross in the sixth minute that had a bit too much pace on it for Russell McLean who headed wide.
Seconds later Rory McAllister bore in on goal but shot straight at the keeper.
The game then went into a lull with neither side able to conjure up a killer pass and create a genuine chance until the 29th minute. A long ball forward by Willie Gibson picked out McAllister but his low drive from an angle was held by Fleming.
A Gibson corner from the left fell to Scott Brown but his shot went wide of the left-hand post.
Peterhead started the second half on the front foot and a Gibson free-kick was headed down to Jason Brown by McLean but his lunge at the ball sent it on to the top of the net.
The Gable Endies’ response was a Templeman lay-off for Sean Dillon but he scuffed his shot wide.
On the hour Jack Leitch had a sniff of goal but his effort was easily gathered by the Montrose keeper.
Back came the visitors and a diving header by Michael Bolochoweckyj spun over but moments later they broke the deadlock.
A quickly-taken free-kick fell to Michael Webster, his shot struck the post and Templeman was on hand to score from eight yards.
Seven minutes from the end Jason Brown headed over another Gibson cross as hope of an equaliser faded, then McAllister lashed a shot over from a tight angle.