The travelling Bees took the lead in the first half through Mathias Jensen, who fired beyond Andre Onana as the United defence failed to clear.
But a breathless six minutes of stoppage time saw the Reds turn things around, thanks to second-half substitute McTominay.
The Scotsman fired home three minutes into the added time, before heading home the winner with virtually the last touch of the encounter.
The Reds began our encounter with Brentford on the front foot, surging forward in search of the opening goal. Operating on the right, Bruno Fernandes planted a handful of teasing balls into the box but to no avail.