The Bees fought back from two goals down to rescue a point in a real game of two halves in the blistering London sunshine.
First-half strikes from Jean-Yves Kouèniate and Armarni Litle saw the visitors race into a two-goal lead at the break, in a half where Darren Currie's side really struggled to get going.
But it was a different story in the second half as the Bees dominated proceedings and clawed themselves back into the game thanks to goals from Ephron Mason Clark and Jack Taylor.
The Bees got off to the worst possible start as Jean-Yves Koueniate tapped home after Scott Loach saved from a Gulls free-kick.
Just two minutes later Josh Walker almost fired Currie's men level as he superbly turned inside the area, however, his shot went just wide of the far post.
Loach on his 400th appearance did well to keep the score to one as he flew off his line to deny Ben Wynter after he stole the ball from Charlie Rowan.
After 11 minutes Walker was through for the Bees but his shot was well saved by Lucas Covolan, the striker was making his first appearance for 8 months and was a danger in the opening exchanges.
On the half-hour mark, the visitors made it two and in some style as Little bent into the top corner from 25 yards out leaving Loach with no chance.
It really wasn't the Bees afternoon in the first half and had it not been for a superb block by Ricardo Santos it would have been three for the visitors before the break.
Just four minutes after the break Mason-Clark halved the deficit as he tapped home after Walker unselfishly squared the ball to him six yards out.
The Bees were almost level on 56 minutes as Sparkes' superb cross was met by J Taylor but unfortunately, he couldn't quite make the desired contact as is volley went straight at the keeper.
With 10 minutes to go Mason Clark was involved again as he narrowly headed over from Alexander's cross, it had the keeper worried but perhaps the substitute could have done slightly better with his effort.
With two minutes left on the clock, the Bees had the equaliser as Jack Taylor sent a powerful drive into the bottom corner with a little help from the left-hand post.
It means its three draws on the spin for Currie's men as they have once again come from behind to salvage what could be valuable points.
They will look to turn a point into victory as they travel to Eastleigh on Saturday, looking to maintain their unbeaten away record.