Kempston were looking to cement their place in the top 5 as Hadley visited Hillgrounds for the first time in their history.
In front of an impressive crowd of 151, the first half hour was fairly uneventful, however Hadley took the lead deservedly on 29 minutes, Peter Rosemin heading in from 6 yards after an excellent cross from the left.
Rovers responded well, equalising just four minutes later. Goalkeeper George Rose pinging a perfect through ball for Ben Baker to lob Ward via the post into the net despite the best efforts of Rovers' Player of the Year Miguel Lopes DeMatos in trying to keep it out on the line.
The Bricks regained the lead on 38 minutes, once again a cross from the left was poked in by Cheik Zidouemba at the near post.
Into the second half and Rovers made a triple sub half way through the half to try and make something happen, Wilson, Bakogeorge and Muyembe introduced for Dummett, Hatch and Stevens, however it was the visitors who extended their lead on 71 minutes. Finley Aldridge finding space in behind and he took his chance very well as he rounded Rose in the Kempston net.
The scoring was wrapped up on 83 minutes, substitute Zacharias Uribarri cut in from the left and found the postage stamp; an excellent finish.
Rovers fall to consecutive home defeats, slipping to 5th whereas Hadley make it two away games on the trot that they have scored four, climbing to 11th.
Rovers are next in action at home on Saturday, as second placed Ware travel to Hillgrounds.