Rovers' 1-0 loss to Notts County means the Bees are two points shy of second-placed Rovers in League One's final automatic promotion spot before they meet at Griffin Park next Saturday.
And the Bees will see this as a missed opportunity against relegated Pools.
Goalkeeper Scott Flinders had to be alert to get two hands to a rising shot from Jake Reeves to push it over, but Pools took the lead after 25 minutes.
Luke James took possession on the left side and sprayed the ball across the area for Jack Baldwin, when his goalbound shot was cleared by Kevin O'Connor the ball fell for James and he picked his spot to fire home.
However the Bees levelled after 39 minutes, Flinders made a flying save from a Jonathan Douglas header but Pools failed to clear and the ball was played into the feet of Marcello Trotta, who was able to turn in the area and convert.
The Bees did not create much in a flat second period, with their best chance coming in the 87th minute when substitute Tom Adeyemi broke into the area but Peter Hartley blocked his shot.