Mallik Wilks pulled a goal back for Barnsley during the second half but the Tykes could not swerve a 3-1 home defeat.
The visitors got off to a flying start with two goals in the opening five minutes.
Butterfield was the first to strike with a well-struck effort from the edge of the area two minutes in.
Radlinger did well to prevent Collins from scoring his second goal of the match, turning the ball wide.
Barnsley's Alex Mowatt tried a long-range effort which went over and Wilks saw his shot from inside the area blocked.
Luton continued to apply pressure, however, with Cornick and Matt Pearson both having shots saved by Radlinger.
It was no surprise when the visitors added a third goal in the 31st minute as a free-kick was headed down and Cornick hammered the ball into the net.
Luke Thomas had an opportunity to reduce the arrears shortly before the interval when he received the ball inside the area but put his shot off-target.
The home side posed an attacking threat in the opening stages of the half, with Mamadou Thiam in the thick of the action, first heading just wide and then firing in a shot from the left-hand side of the area which was palmed wide by Simon Sluga.
Wilks (72) did find the back of the net, firing in after Mowatt played the ball across the box.
Cameron McGeehan just failed to get a touch to a Wilks header following a corner as the hosts went in search of a second to put themselves in contention.
Thiam spooned the ball well over from inside the area following Green's lay-off.
Barnsley, who beat Fulham on the opening day of the season, have now lost four of their last five games.