Robbie Weir gave the visitors the lead inside the half hour in Saturday’s League One clash at Griffin Park, heading home Andy Robinson’s pin-point cross unmarked at the far post.
Brentford striker Clayton Donaldson wasted a gilt-edged chance to haul the Bees back into it just before the break, firing his effort straight at Owain Fon Williams.
Gary Alexander saw a speculative effort bounce off the bar for the hosts, but that was the closest Uwe Rosler’s side came to breaking their duck.
Any hopes of revival were ended a minute after the restart when Robinson lashed home an unstoppable dipping drive from 30 yards that left Brentford keeper Richard Lee with no chance.
Lucas Akins was a constant threat for Tranmere and saw two efforts go close to extending the lead, one of them flashing into the side netting.