After a fairly flat first 45 minutes for the Blades collectively, an increase in tempo and intensity in the second half saw them run out comfortable winners thanks to two goals in the space of three minutes from Brewster and defender Jack Robinson, his first since 2018.
Luton also ended the game with 10 men after Reece Burke saw red, for bringing down Brewster as he looked to break away on goal.
And Heckingbottom said afterwards: “The front boys played well. I wanted more from Rhian and Iliman [Ndiaye] after the first half.
“They’re big talents but they have to do their jobs in and out of possession. He took that on board in the second half, worked closer to Billy. Delighted he got the goal and where he got the goal, in between the posts.
“We need him in there more. We still want more and he’ll certainly be pushed.
“We showed him some clips at half-time about what we needed from him and he delivered that in the second half, which is credit to him.
“We spoke to the experienced boys about managing the game, so we earned the right to see the game out. If we need to slow it down, then we do.
“But we need to inject energy when it was right because we had the extra body there.”