Rotherham's recent run had given them a bit of breathing space above their relegation rivals but they remain firmly in the scrap to stay up following this defeat.
Luton threatened first in the game and it took a brave block from Tyler Blackett to prevent Marvelous Nakamba's powerful strike from testing Josh Vickers.
Both teams then seemed to cancel one another out with neither goalkeeper being forced into a save for a large period.
Morris would have been disappointed not to hit the target when his flicked header from Pelly-Ruddock Mpanzu's cross landed on the roof of the net.
Luton were really starting to press before the break and it was only an incredible last-ditch save from Vickers that denied Amari'i Bell what looked like a certain goal.
Morris then carved out the opener himself after 45 minutes. The big striker cut back inside onto his left foot and fired into the roof of the net from an awkward angle.
Luton picked up where they left off in the second half and doubled their lead after 47 minutes.
Wes Harding handled a cross from Cody Drameh and Woodrow stroked home after his initial penalty had been saved by Vickers.
Rotherham tried to rally and a long-range free-kick from substitute Domingos Quina momentarily had Ethan Horvath scrambling before it drifted wide.
A mazy run for Quina then resulted in a chance for Jamie Lindsay but his shot from the edge of the area was blocked.
Luton could have put the game beyond doubt thanks to a swift move involving Drameh and Mpanzu which ended with Allan Campbell having hit shot deflected off target by Richard Wood.
Luton skipper Sonny Bradley rose highest from Drameh's corner but Vickers managed to grasp his powerful header.
The visitors were still hunting a third goal and substitute Louie Watson tried to turn in a cross with his backheel but it was kept out by Vickers at his near post.
Rotherham were the ones pushing in the seven minutes of added-on time but Luton resiliently saw off a number of crosses into the box.
The final chance of the game fell the Millers' way but Quina's free-kick from right on the edge of the box took a deflection and drifted harmlessly wide.