Rhodes was on target with two headers either side of the break as the Terriers tore Uwe Rosler's side to shreds to extend their unbeaten league run to 36 matches.
Lee Novak and Gary Roberts weighed in with the other second-half strikes to give the visitors a score line their dominance deserved and it might have been more as the woodwork came to the Bees rescue on at least two occasions in a one-sided second half.
Rhodes struck first when he powered home a header back across goal to give his side the advantage just before half-time and Novak stretched the lead in the 70th minute when Damien Johnson played him in through a square Brentford back four.
Novak turned provider minutes later when his pin-point cross found Rhodes, who headed home from close range, and Roberts completed the rout with just over 10 minutes remaining when he hammered home after Rhodes' effort had cannoned back off the post.
Brentford managed just one shot on target but Ian Bennett blocked Niall McGinn's close range effort.