Murphy’s two-day-old son, and proud new mum Lisa, were among a crowd of 40,000 at Wembley on Sunday to see the 30-year-old defender thump in the first-half winner.
Murphy junior may not remember too much about his first football match, but his father will not tire of telling him all about it in the years to come.
The long-serving centre-half settled the match with a stylish finish from a corner after just 12 minutes.
It meant Carlisle, making the 600-mile round trip to the national stadium for the second successive year, went one better than last season’s defeat by Southampton.
For Brentford, the journey to Wembley consists of a few stops on the Metropolitan Line, but the trip home will now seem just as long as their opponent’s.
To add to their misery they had midfielder Toumani Diagouraga sent off late in the second half.
Their rookie goalkeeper Simon Moore was starting only his fourth senior match and quickly found himself in the thick of the action with a fine diving save to keep out Francois Zoko’s header.
But the youngster could do nothing to prevent Carlisle scoring from the resulting corner.
Zoko challenged for James Berrett’s cross and the ball fell to Murphy eight yards out to control on his knee before crashing it past Moore high into the net.
Brentford tried to hit straight back and Sam Saunders curled a free-kick wide from 25 yards.
Carlisle were dealt a blow midway through the half when midfielder Ben Marshall left the field on a stretcher after he was fouled by Adam Reed.
Leon Legge followed Reed into the referee’s notebook for a foul on Zoko, prompting a deep conversation between Carlisle boss Greg Abbott and the fourth official.
Saunders fired another shot wide as the first half drew to a close but the Bees were distinctly below par.
Nicky Forster, leading Brentford out at Wembley after just two months as a manager, threw on substitute Marcus Bean at half-time and his side improved after the break.
They came agonisingly close to grabbing an equaliser 10 minutes into the second half when Jeffrey Schlupp burst through.
The teenager, who scored both goals when Brentford beat Carlisle in their League One meeting nine days ago, tore past Lubomir Michalik and cut inside but his low drive crashed against the post.
Karleigh Osborne was then inches away from a dangerous Saunders cross as the Bees pressed.
But Diagouraga, who had been booked moments earlier, scythed down Tom Taiwo three minutes from time and was sent off.
Legge put a header wide in stoppage time, but moments later the final whistle blew to give Murphy and Carlisle something else to celebrate.