Two goals from Daniel Ward (14,15) gave Terriers an early lead, before Jeffery Schlupp replied in first-half stoppage time before equalising on 50 minutes.
The home crowd barely had time to settle down before Lee Novak fired Town back in front, then Lewis Grabban made it 3-3.
Benik Afobe continued the amazing goals spree when he put Town back in front on 68 minutes, but Brentford refused to lie down and Grabban equalised once more.
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