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 Derek Holmes' attempts to clear a David Hunt cross bounced off a defender and into the path of Bojic who fired a left-foot 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 20-yard drive was tipped over full stretch, but that was the best Carlisle had to offer.
On the stroke of far time McGleish should have added a second for Northampton, but he headed inches wide when well placed.
The Cumbrians started the second half brightly and had a penalty appeal turned down when Carl Hawley was sandwich between two defenders in the box but referee Clive Oliver waved away the furious appeals.
From then Carlisle huffed and puffed but the Cobblers defence would not be moved and the Cumbrians were reduced to having a series of poor long range efforts and futile penalty appeals.
Not one of the home side's second half chances forced Harper into a meaningful save and 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 20 yards only to see the ball fall agonisingly past the post with Harper beaten.