Three years after last lifting the trophy, the Saints got their hands back on the silverware as fortune smiled on midfielder Brobbel.
Golden Boot winner Greg Draper had opened the scoring early on to put the Saints on course of a seventh cup triumph, while at the same time completing a league and cup double for Scott Ruscoe’s in-form side.
Nomads, the Welsh Premier runners-up, had plenty of possession and promising openings, but it proved a frustrating afternoon that ended with Andy Owens being sent off for his second booking 10 minutes from time.
Unbeaten in 22 games, TNS sounded a warning in the fourth minute when Jon Routledge chipped into the box from the right and Brobbel nodded over at full stretch.
But the league champions did not have long to wait before taking the lead through the predatory Draper two minutes later.
Chris Marriott floated a neat pass down the left channel to Adrian Cieslewicz whose low strike was parried by keeper John Danby only for the rebound to fall for Draper who made no mistake from close range.
After a slow start, the Nomads launched a couple of promising raids, with former TNS striker Mike Wilde dragging one shot wide and Callum Morris seeing a goalbound effort blocked, while they also had couple of penalty shouts turned down.
However, just as the Nomads were getting back into the game, they were stung in the 32nd minute when Brobbel’s free-kick from out on the left deceived Danby before finding its way into the top of the net.
Michael Bakare almost responded for Quay in similar manner moments later with a curling free-kick from the right, but Saints keeper Paul Harrison was able to tip the ball over the bar.
The Nomads had their fair share of goalmouth skirmishes, with Harrison making a strong save low down from Jamie Insall’s acrobatic effort right on half time.
Quay – whose head coach Craig Harrison won four Welsh Cups with TNS – came out for the second half with purpose as John Disney steered a shot just wide from the edge of the box.
TNS, however, continued to pose a threat on the break, with Brobbel’s low strike being met by a smart one-handed save from Danby.
And hopes of a Quay fightback faded further on the hour when another free-kick from Brobbel from wide on the left found its way through a congested goalmouth and in past Danby.
Blaine Hudson and sub Dean Ebbe both headed wide as the Saints chased a fourth, while Nomads had Owens dismissed for his second booking after diving in the box 10 minutes from time.