In a tight encounter, the Cumbrians started brightly and created the first opening in the eighth minute when Derek Holmes swivelled on the edge of the area and got in a shot that was smartly saved by Alan Julian in the Stevenage goal.
When Borough hit back Anthony Elding smashed a shot just wide as the Carlisle defenders gave him time and space to line up his effort.
Julian then got down well to keep out Glenn Murray's sweetly-struck volley while Borough's Darryn Stamp should have done better in the 15th minute with a good opportunity.
The only goal of the game came in the 23rd minute when veteran left-back Tom Cowan dinked a cross in to the area for Murphy to head past Julian – his eight goal of the season.
Three minutes later Elding's touch let him down when he looked to be in on goal and then Stamp, virtually under the crossbar, was unable to latch on to a tantalising cross.
Carlisle almost scored again in the 40th minute when Murray's shot was deflected just wide as Julian struggled to get across his goal. From the corner Jason Goodliffe headed the ball over his own bar as Danny Livesey's effort looked to be creeping into the net.
The second half became increasingly scrappy as Stevenage tried to hit back and chances were few and far between.
In the 53rd minute Brendan McGill dragged a shot wide for Carlisle and on the hour Borough striker Elding blasted a volley way over the bar after Dino Maamria had acrobatically kept the ball in play.
Holmes wasted a great opportunity to double Carlisle's lead in the 66th minute when he miskicked in front of goal after being set up by Cowan.
Four minutes later Jon Brady fired a free-kick over the bar from a promising position as Borough started to get on top.
Stevenage's best chance of an equaliser came in the 78th minute when a McGill error let in Michael Warner but Matt Glennon did well to keep out the shot with his legs.
But Carlisle hung on and will now be playing the likes of Rochdale and Darlington again next season.