Stockport bolstered their survival hopes while sending Kettering closer to relegation with a comfortable victory.
Danny Hattersley converted Andy Halls' cross to put the visitors in front.
Sean Newton doubled their lead with an 18-yard free-kick before Poppies player-manager Ashley Westwood headed in from Charlie Wyke's centre.
But Kettering's hopes of launching a comeback were dashed when Cameron Darkwah drilled in a spectacular last-minute effort.
Westwood's side are now nine points adrift of safety in the Blue Square Bet Premier with just five games of the season remaining.
VIEWS FROM THE DRESSING ROOM
Kettering Town caretaker manager Ashley Westwood told BBC Radio Northampton:
"I'm as disappointed as I've been throughout my career at the minute.
"We were 2-0 down and well beaten in the first half. We weren't winning second balls or holding the ball up front and we were constantly on the back foot.
"We were the better team in the second half, but they weren't going to throw the kitchen sink at us with a 2-0 lead.
"We're going to fight all the way. (I need) a reaction, some desire and passion. We'll be trying to do the fans justice and make them proud of us for what we'll show in the next five games."