Rory McAllister netted from the spot three minutes before the break but substitute Chris Millar levelled the scores within four minutes of the restart for the Perth side before Danny Invincibile headed the SPL side into the lead.
However, McAllister earned his side a deserved replay with an excellent finish from an acute angle with 12 minutes left on the clock.
St Johnstone named the same team that drew 1-1 with Hibernian as they looked to avoid an upset, though midfielder Millar returned from a hamstring injury to take his place on the substitutes' bench.
McAllister, Neil Janczyk, Kevin Byers and Gerry McLaughlin recovered from injuries to take their places in the Brechin starting XI.
Brechin survived an early scare after six minutes when Liam Craig's shot came back off the underside of the crossbar.
However, the home side looked far from overawed against their top-flight opponents and went desperately close to breaking the deadlock when Byers' low drive hit the post a minute later.
The match became increasingly scrappy on a pitch far from conducive to good football, with St Johnstone's Jamie Adams picking up the first booking of the match after 23 minutes for dissent.
The home side had a penalty claim turned down when Graham Gartland and McAllister collided in the box before Brechin's veteran stopper Craig Nelson made a fine stop to deny Invincibile.
Brechin had the chance to open the scoring just before the break when Murray Davidson tripped Janczyk and this time referee Steve Conroy did point to the spot.
Craig Molloy's cool conversion first time around was ruled out for encroachment before McAllister stepped up to send Peter Enckelman the wrong way.
The visitors made a change at the break with Adams making way for Millar, and the substitute made an immediate impact.
Craig's deflected cross was headed away by Ewan Moyes into the path of Millar, who drilled the ball into the bottom corner from the edge of the area.
St Johnstone took the lead after 63 minutes when Danny Grainger's in-swinging corner was powerfully headed home by Invincibile.
With 12 minutes remaining the tireless McAllister brought Brechin level with a fantastic finish across Enckelman from an acute angle to the delight of the home support.
St Johnstone should have scored a late winner but substitute Stephen Reynolds somehow blasted over with the goal gaping.