Both sides were looking for a much needed victory, but ultimately battled out an uninspiring stalemate.
Ryan Thomson and Steven Bell returned to the bench from suspension and injury respectively, as Stevie Farrell showed loyalty to the starting eleven which defeated Airdrieonians.
Young prospect Kyle Turner kept his place, Craig Malcolm joining him in midfield with Mark McGuigan selected as the lone forward.
McGuigan didn't have to wait long for his first opportunity, but could only bundle Agnew's ball over the bar on the volley with barely a few minutes on the clock.
Alan Trouten tried a speculative effort for the hosts from distance which Cammy Belford was equal to.
Willie Gibson was determined to test stand-in keeper Patrick O'Neil, who didn't look out of place on his 8th appearance for Brechin.
The backup goalie twice held firm at the far post as Gibson floated in goalbound efforts from the left flank.
Scott Robertson was next to try his luck with a half volley from the right hand side 20 yards out, but his shot flashed past the foot of the left hand post.
The hosts grew into the game as the half wore on.
Visiting keeper Cameron Belford denied Ally Love, and was relieved to see Liam Watt shoot wide twice, the latter from a free kick in a promising position.
The Blues keeper chested away Andy Jackson's straightforward effort to bring an uninspiring first 45 minutes to a close.
Thankfully, the second half was a slightly livelier affair.
Gibson was the man who looked most like scoring, but Brechin keeper O'Neil was on hand once again to touch his effort from the free kick past the post.
A string of second half saves from Belford - including a magnificent stop at close range from prolific striker Andy Jackson - set up a tense finale.
Substitute Amadou Kassaraté won a free kick down the left hand side, and Gibson's pinpoint delivery was headed just over the bar by defender Morgyn Neill.
Jackson's piledriver from the edge of the box sailed off target as both sides chased a winner.
The Blues would have two more chances to win the game in the dying moments as the travelling support urged them on. Scott Agnew drilled a low strike bound for the bottom right corner, which the keeper did well to turn past the post.
And Malcolm got a touch on the resulting corner, only to see the ball sail agonisingly wide.
However, with Stenhousemuir defeating Peterhead at Balmoor, the draw edges Stranraer further clear of 9th place.
The Blues go into next week's game at Alloa next Saturday knowing that win would secure League 1 football next season.
Stranraer: Belford, Pettigrew (Wilson 77), Dick, Barron, Robertson, Neill, Malcolm, Agnew, Gibson, Turner (Thomson 60), McGuigan (Kassaraté 68).
Not used: Currie, Bell, Morena, Donald, Kemp.
Booked: Neill, Barron, Malcolm.
Brechin City: P. O'Neil, McLean, Dyer, Fusco, Lynas, Dale, Trouten, Graham, Watt, Jackson, Love.
Not used: Caldwell, Ford, C. O'Neil, Dods.
Booked: Watt, Fusco.
Referee: Gavin Ross