Ben May was provider and goalscorer for The Bees as Stephen Evans was controversially dismissed.
The match turned on the 10th minute red card handed to the Welshman for his challenge on Sean Connelly. The Bees were already behind two minutes earlier due to slack marking, Rovers striker Eugene Dadi evadng the challenge of Frampton to slid the ball past Smith.
Stephen Hunt equalised in the 18th minute, Ben May's quality through ball giving the Irishman a chance to tuck the ball past Achterburg.
Fourteen minutes after the break Tranmere went ahead, again Dadi rising unmarked to head home. However, two minutes later Ben May put The Bees on level terms, his quick turn and shot giving his sixth goal of the campaign, In the 69th minute, May saw Achterburg off his line and tried a lob from 40 yards that the Rovers' goalkeeper did well to palm onto the crossbar.
Simon Howarth, who was a Bees transfer target five years ago, broke his fibula in a challenge with Brentford defender Andy Frampton and was taken to hospital.
Despite late efforts by Alex Hay and Ben May, the match ended level.