The Cobblers finally lived up to their pre-season billing as League Two favourites and performed well to build on their League Cup victory over QPR in midweek.
Neither side managed to stamp their authority on the match with Bojic's strike being the only clearly cut chance throughout the 90 minutes.
On 37 minutes the Blues gifted the visitors a goal as Derek Holmes' attempts to clear a David Hunt cross bounced off Zigor Aranalde and into the path of Bojic who fired a left-foot shot past Anthony Williams from eight yards.
Before then Holmes had gone close for Carlisle, while Northampton's Scott McGleish ran clean through only to fire wide from 20 yards.
Adam Murray also forced a great save from Town keeper Lee Harper when his rasping drive from the edge of the box was tipped over at full stretch, but that was the best Carlisle had to offer as they struggled to break down a strong Northampton defence.
On the stroke of half-time McGleish should have added a second for Northampton, but he headed inches wide from a right-wing cross when well placed.
The Cumbrians started the second half brightly and had a penalty appeal turned down when Karl Hawley was sandwiched between two defenders in the box but referee Clive Oliver waved away the furious appeals as for the second home game in a row United had what looked like a clear-cut penalty turned down.
From then Carlisle huffed and puffed but the Cobblers defence would not be moved and the Blues were reduced to having a series of poor long range efforts that did more damage to the Warwick Road roof. Too often the Blues again resorted to long diagonal balls from the back to Holmes and Hawley and only looked dangerous when Brendan McGill got the ball out wide and put in some teasing crosses. McGill though seemed to spend most of the game with his arms in the air in frustration as the ball bypassed him on its aerial route to the edge of the visitors penalty area.
Not one of the home side's second half chances forced Harper into a meaningful save and Adam Murray in particular was guilty of firing half a dozen shots into the crowd with Carlisle pushing forward.
Town's Ian Taylor almost made the game safe for the Cobblers but his back post header was well saved Williams.
And with the Brunton Park fateful screaming for an equaliser substitute Glenn Murray almost grabbed a point at the death.
Brendan McGill's mis-hit cross found Murray with his back to goal and he flicked a shot over his shoulder from 12 yards only to see the ball fall agonisingly past the post with Harper beaten.
So another good chance for a second home victory goes begging with the Blues bossing the majority of the game but completely unable to turn possession into clear-cut chances. A goalpoacher is obviously a priority before the transfer window closes on Wednesday but on today’s evidence even the available Michael Owen would have struggled to bag a goal on a day when the ball always seemed to drop to a Northampton defender in their own box and United wouldn’t have created a clear opportunity if they had played until midnight.
Let’s hope the lads can keep their unbeaten away record in the league on Bank Holiday Monday when they visit a big, physical Lincoln outfit at Sincil Bank.
Northampton boss Colin Calderwood was relieved after the game in which he responded to abuse from the Paddock by swearing back at them himself and complaining to the fourth official, you’d have thought someone with the level of experience Calderwood has would know not to get involved.
He said: "It's almost a typical away performance as we performed heroically during their onslaught in the second half. We are delighted with the win and we need to keep on getting wins like this to be up there at the end of the season.
"By hook or by crook we got things clear and the character of the team really shone through. It was backs to the wall stuff, but we responded well to our mid-week victory and, although Carlisle might be disappointed to have taken nothing out of the game we had the better chances in my opinion we deserved to win."
Carlisle assistant manager Dennis Booth said: "We are very disappointed, especially after last week's performance against Wrexham. We started okay but after their goal we couldn't open up their defence and it was disappointing not to make the goalkeeper work.
"The goal knocked us back and, although Karl Hawley might have had a penalty, we can't blame the referee."