Stranraer picked up their first clean sheet since October as they made it two games unbeaten in the space of a week.
The Blues came into the contest boosted by an impressive win at The Spartans on Tuesday night.
Manager Chris Aitken was forced into one change as Chris McQueen came into the team in place of the unavailable Adam Cummins.
The visitors made the trip south as the form team of Scottish League Two and made one change of their own as Innes Lawson dropped out in favour of Ouzy See.
In a game of relatively few chances, Stranraer had the majority although Edinburgh City probably edged possession in the first half.
The first of those opportunities came just before the quarter hour mark when the visitors struggled to get the ball clear on the edge of their own box.
Eventually, Deryn Lang found enough space to get a shot away but it curled just the wrong side of the post, with goalkeeper Mark Weir a spectator.
Four minutes later and the impressive Elliot Dunlop almost came up with a stylish individual goal.
He skipped away from one defender before cutting inside another, only to place his shot too close to the visiting number one.
Closest for the visitors was James Stokes, who pulled a shot across goal and wide of the target.
Then, in first half stoppage time, Edinburgh were presented with another good opportunity.
Tomas Brindley slipped out wide and lost possession before Jason Jarvis called Robbie Mutch into action.
No goals at the break meant all was still to play for in the second half as both clubs attempted to take all three points.
Stranraer dominated possession in the second half but could not find the breakthrough.
The best chance fell once again to Dunlop, who cut in from the left into the box.
Goalkeeper Weir was out quickly and got enough of a block to see the ball spin wide of the target.
The home side forced a number of corners but time and again Weir punched clear under pressure inside his six-yard box.
Four points out of six marks a good return for Stranraer, who now travel to Stirling Albion looking to make it three games unbeaten.
Stranraer: Mutch, Robertson (Foster 83), Brindley, Ross, McQueen, Gallagher, Dunlop, Russell, Hawkshaw (McKnight 75), Grant, Lang (Guthrie 83).
Not used: Adam and Pazikas.
Edinburgh City: Weir, Gormley, Mitchell, Lynch, Stokes, Jones, Young, Jarvis (Hamilton 70), Wells, Grigor, See.
Not used: Scally, Walker, Rennie, Pitt and Beveridge.
Referee: Ryan Lee
Attendance: 381
HT: 0-0
Photos: Bill McCandlish
