Carlisle manager Keith Curle had talked up the importance of the game to his side and they started well, taking the lead through Archibald-Henville on 17 minutes.
Chris Wilder, meanwhile, had challenged his players to respond to the criticisms he made of them after last weekend's defeat by Plymouth Argyle and they bounced back well from going behind to make a number of chances.
Marc Richards equalised with almost the last action of a first half that saw four yellow cards issued, converting from the penalty spot after Evan Horwood had been fouled in the penalty area.
Richards and Ivan Toney continued to cause problems for Carlisle after the break but the crucial third goal of the game was scored by the home side on 61 minutes as Brad Potts netted, sparking a double substitution for the Cobblers with widemen Hackett and Mohamed entering the fray.
Lawson D'Ath was the final throw of the dice, replacing Ben Tozer on 78 minutes while seven minutes of added time also gave the Cobblers hope but it was not to be despite a host of chances going their way.
Match Reaction: "We were good from box to box, we created enough chances and the shape of the team was good,” said Northampton manager Wilder after the game.
"But we can’t keep it out of our net and when we get at the top end of the pitch we can’t put it in their net - it’s pretty straightforward stuff."