A goal in either half saw Livingston step up their pursuit of a play-off place as rock-bottom Brechin remained winless.
City, though, almost made the perfect start when an early shot by Connor McLennan drew a save from Neil Alexander.
Instead the home side found themselves behind when McLennan was judged to have fouled Jackson Longridge in the box and Craig Halkett drilled the penalty low into the corner of the net, giving Graeme Smith no chance.
Livingston went on to enjoy large periods of possession without seriously threatening to add to their lead before the break.
It was a similar pattern on the restart with Declan Gallagher heading over from a good position before Steven Boyd and Scott Robinson sent efforts narrowly wide.
Robinson, though, found his range as the pressure finally told on the hard-pressed City defence, the Livingston midfielder pouncing on a loose ball to score from ten yards. Brechin refused to throw in the towel and might have grabbed a lifeline when Paul McLean found space to shoot but his effort was too close to Alexander.
Euan Smith also sent a late effort narrowly wide but there was to be no consolation for the Glebe Park side.