Leeds left it late to snatch a 2-1 win at struggling Luton which helped them climb back into the Sky Bet Championship automatic promotion places.
Although Leeds dominated the early stages in terms of possession, it was Luton who had the first effort after 20 minutes, Pelly-Ruddock Mpanzu firing over the bar from just outside the box.
Midway through the half Bamford went closest for Leeds, as a quick visiting break saw his left-footed effort force James Shea into an awkward save.
Leeds then began to take a real stranglehold on proceedings, with Bamford's close-range attempt hitting the upright, before Shea made a superb double save to keep out Kalvin Phillips' 20-yard strike and Jack Harrison's follow-up.
Mateusz Klich and Luke Ayling both had efforts fly wide while, with 40 minutes gone, Bamford's header was too close to Shea, before the home keeper made an excellent save from Tyler Roberts' deflected effort.
Moments before half-time Brown curled over for Luton but, in the second period, United had the lead after 50 minutes with a goal of real controversy.
Brown appeared to be clipped when on the ball for Town, only for referee John Brooks to give nothing. Leeds counter-attacked with clinical precision and Bamford rifled past Shea at his near post.
Harry Cornick's effort was saved by the keeper, before Luton thought they had the lead but Matty Pearson's goal was ruled out by a late linesman's flag.
Bradley whizzed one over from the edge of the box yet Bamford should have made it 2-1 on 64 minutes, volleying waywardly from just eight yards out.
Luton tried for a winner, Andrew Shinnie's low drive gathered by Casilla, but United kept on pushing in the closing stages, bringing on Tottenham's Jack Clarke for his first league appearance of the season.
Shea denied Klich twice in the closing stages, as it looked like he would be the hero until Bamford pounced, with the help of Pearson.
Town should have left with a point though, Dan Potts heading a gilt-edged chance wide with the last kick as Luton slumped to another loss.