Rhodes, who produced a quality finish five minutes after the restart to lift Town back into the automatic promotion places, has scored 13 goals in his last seven matches.
Brentford went ahead in the 21st minute when Town skipper Peter Clarke pulled over Marcus Bean in the box. Gary Alexander sent keeper Ian Bennett the wrong way from the penalty spot.
Brentford doubled the lead in the 29th minute when Niall McGinn showed a great burst of speed to beat Gary Naysmith to the byline and crossed low to the near post for Alexander to fire home his second from close range.
Town winger Gary Roberts' powerful shot was tipped onto the crossbar, but Huddersfield scored from the resulting corner, striker Alan Lee barging into Brentford goalkeeper Richard Lee and nodding the ball over the goalline for his 100th league goal.
Town levelled in first-half stoppage time through Jamie McCombe's looping header and Roberts hit the crossbar again before Rhodes won it in the 50th minute when he dribbled past Marcel Eger and curled a right-footed shot past Lee into the far corner.