After an even opening 25 minutes the game burst into life with four goals before the interval. First, Danny Ings converted a low cut-back to make it 1-0 but Josh Dasilva's sweet finish into the bottom corner levelled things up instantly.
Ollie Watkins put Brentford ahead just before the break but again it was a short-lived lead, Ings grabbing his second of the game.
After the restart, David Raya made a crucial one-on-one save seconds before Watkins saw a close-range effort blocked as both sides created chances. However, it was Saints who took the points 14 minutes from time as Nathan Redmond slotted home the rebound after a shot cannoned back off the post.
Lincoln City and Crawley Town open their campaign tomorrow night before The Bees take on The Imps on Tuesday night in the second Group O game.