The welcome victory took Rotherham to minus three points but leaves rock-bottom Luton with a massive task to avoid the drop after their 30-point deduction.
Rotherham missed an early chance to break the deadlock when Reuben Reid headed down a cross from Pablo Mills. Drewe Broughton tried to squeeze in a snapshot but as he lost his balance the big sriker could only scoop the ball over the bar from six yards.
Rhodes then showed a burst of pace and fired into the side-netting as keeper Dean Brill forced him wide.
And when Rotherham's pressure saw the ball break to Mills, he flicked a shot with the outside of his right foot just wide before Rhodes headed Mark Lynch's free-kick off target.
Lynch then drilled a shot wide while at the other end Rossi Jarvis' corner was headed over the bar by Michael Spillane.
Marc Pugh did some good work on the left before rifling in a low cross that deserved better, but Rotherham cleared.
Three minutes before the break Luton had the best chance of grabbing an early goal when Keith Keane produced a 25-yard volley that flew straight at home keeper Andy Warrington.
Ten minutes into the second half another chance came Rotherham's way when Andy Nicholas produced a long throw into the box for Ian Sharps but the defender's header dropped over the bar.
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On the hour mark, Rhodes (right) completely mis-hit a cross from the left 40 yards out and it went over Brill as he desperately back-pedalled.
Reid could have added a second but for a super save by Brill and when Reid produced another snap-shot close in, it was blocked on the line.
Moments later Rhodes hit a blistering drive but was denied by another fine stop from Brill.