Robinson was handed his first start of the season by manager Mark McGhee and duly obliged with a well-taken volley on 66 minutes.
McGhee also handed a home debut to West Ham youngster Tony Stokes in the centre of midfield in what was a youthful looking Brighton side.
In an uninspiring first period it was the strong and muscular Gillingham who had the balance of the play.
Brighton did find themselves in the final third of the field on a number of occasions but wide men Robinson and Alex Revell failed to deliver a telling contribution.
The lively Dean McDonald was the main fulcrum of attack for the away side and when he cut across three Brighton defenders and laid the ball off to Andrew Crofts on 33 minutes, the midfielder should have done better with his effort which rolled tamely wide
Ten minutes later and Crofts was involved again, this time choosing to go alone from long distance but Wayne Henderson was equal to his strike tipping it round the post.
Gills' boss Ronnie Jepson appeared to have said some strong words at half time as his side lurched forward in search of the first goal.
Captain Michael Flynn released lively winger Matthew Jarvis on the break off a Brighton corner. Jarvis raced away from the Brighton defence but Irish International Henderson was equal to his effort on goal.
Minutes later and McDonald attempted an audacious lob from just outside the area, but was unlucky to see it ripple across the top of the Brighton net.
Gillingham's brief glut of chances seemed to spark the home side, and Robinson, into life.
Brighton-born Robinson, who made his debut for the Seagulls aged 16, drove in from the left-hand side and unleashed a stinging right-foot shot which to his disappointment flew just wide of the far post.
His dejection though was short-lived as he made a timely run into the box just two minutes later to seal the win. The impressive Paul Reid exchanged passes with Dean Hammond and crossed from the touchline for Robinson to volley in to the far corner of the net.
Gillingham attempted to rally in the last ten minutes but Jarvis wastefully put a header wide as Brighton maintained a 100% record for the start of the season.