Rhodes scored on his full Scotland debut against Australia earlier in the month and netted a stoppage-time penalty to help the Terriers to their first point of the campaign at home to Nottingham Forest on Tuesday night.
The 22-year-old made it three in three with his fine second-half strike as Huddersfield secured their first home win over cross-Pennine rivals Burnley for 56 years.
The opening goal of the game at the John Smith's Stadium had come in controversial circumstances from Joel Lynch on seven minutes.
After a fast break from the home side resulted in them winning a corner, Oliver Norwood sent an inswinging delivery from the right to the near post and defender Lynch rose highest to head in his first goal for the club since joining in the summer.
Burnley were left remonstrating with the officials, however, as they felt that Joseph Mills had cleared the ball off the line, but the assistant referee said the ball had crossed it and the goal was awarded.
The Clarets almost fell further behind as Rhodes twice went close with headers for Huddersfield.
Sean Scannell floated a lovely cross onto the head of Rhodes, but his first effort came back off the crossbar, before connecting with another Norwood corner 10 minutes later which goalkeeper Lee Grant kept out with a brilliant point-blank save.
Eddie Howe's men were struggling to get a foothold in the game against the Championship new boys, although they did have the ball in the back of the net on the stroke of half-time only for David Edgar to be ruled offside.
After dominating the first half, Huddersfield continued to impress after the interval and Keith Southern was the next to go close as his effort from distance deflected just wide.
The all-important second goal then arrived for the hosts on 58 minutes as Rhodes rifled the ball into the top right-hand corner from 12 yards out to give Grant no chance in the Burnley goal.
The visitors twice went close to pulling a goal back as first Kieran Trippier's inviting cross was headed on to the roof of the net by striker Charlie Austin and then Ross Wallace curled a free-kick just over the crossbar.