Dylan Mackin's clinical finish was added to by Scott Pitman's strike just before half-time as Livi took control.
Kalvin Orsi tricked his way past defender Alan Lithgow and finished to halve Brechin's deficit.
And Finn Graham fired home to level matters just after the hour mark at Glebe Park.
Match ends, Brechin City 2, Livingston 2.
Second Half ends, Brechin City 2, Livingston 2.
Attempt missed. Nicky Cadden (Livingston) left footed shot from a difficult angle and long range on the right is too high from a direct free kick.
Foul by Gary Fusco (Brechin City).
Dale Carrick (Livingston) wins a free kick on the right wing.
Paul McLean (Brechin City) wins a free kick in the attacking half.
Foul by Declan Gallagher (Livingston).
James Dale (Brechin City) is shown the yellow card for a bad foul.
Foul by James Dale (Brechin City).
Shaun Byrne (Livingston) wins a free kick in the attacking half.
Attempt missed. Nicky Cadden (Livingston) left footed shot from outside the box is close, but misses to the left.
Andrew Jackson (Brechin City) wins a free kick in the defensive half.
Foul by Alan Lithgow (Livingston).
Corner,  Livingston. Conceded by Paul McLean.
Attempt blocked. Scott Robinson (Livingston) right footed shot from the centre of the box is blocked.
Attempt missed. Dale Carrick (Livingston) right footed shot from the centre of the box misses to the right.
Corner,  Livingston. Conceded by Willie Dyer.
Isaac Layne (Brechin City) wins a free kick in the defensive half.
Foul by Alan Lithgow (Livingston).
Corner,  Livingston. Conceded by Aron Lynas.
Substitution, Livingston. Nicky Cadden replaces Raffaele De Vita.
Hand ball by Jackson Longridge (Livingston).
Aron Lynas (Brechin City) wins a free kick in the attacking half.
Foul by Jackson Longridge (Livingston).
Jackson Longridge (Livingston) is shown the yellow card for a bad foul.
Attempt missed. Isaac Layne (Brechin City) right footed shot from outside the box is close, but misses to the left.
Paul McLean (Brechin City) wins a free kick in the attacking half.
Foul by Dylan Mackin (Livingston).
Aron Lynas (Brechin City) is shown the yellow card for a bad foul.
Foul by Aron Lynas (Brechin City).
Dale Carrick (Livingston) wins a free kick in the attacking half.
Substitution, Brechin City. Isaac Layne replaces Kalvin Orsi.
Willie Dyer (Brechin City) is shown the yellow card for a bad foul.
Foul by Willie Dyer (Brechin City).
Dale Carrick (Livingston) wins a free kick in the attacking half.
Kalvin Orsi (Brechin City) wins a free kick in the attacking half.
Foul by Craig Halkett (Livingston).
Aron Lynas (Brechin City) wins a free kick in the attacking half.
Foul by Declan Gallagher (Livingston).
Attempt blocked. Alan Lithgow (Livingston) right footed shot from outside the box is blocked.
Brechin City came from two goals down to earn their first point in this season's Championship as Livingston were denied a maiden league win.