The Blades ended a four match winless streak with a deserved victory on the south coast.
On one of a number of long-distance trips in the U18s league, Travis Binnion's young side produced an excellent team performance to enjoy the long coach journey home.
Brighton started the game well but didn't take a couple of half-chances early on. The Blades grew into the game and looked a threat on the counter attack, through Coustrain, Cockerline and De Girolamo.
Both De Girolamo and Coustrain worked the home goalkeeper from distance. Cockerline had a good chance when breaking into the box and from his blocked shot, United opened the scoring. From the resulting corner on 25 minutes, EVANS headed home at the back post.
The rest of the half followed the same trend, Brighton on top in terms of possession and United looking the more dangerous on the counter.
The Blades really should have had the game sewn up within 20 minutes of the restart. Chances fell to De Girolamo and Ramsey but poor decisions or execution spared Brighton.
Finally the Blades did put some distance between themselves and Brighton. De Girolamo regained the ball in the opposition half, drove at the defence before sliding Coustrain in and he finished well past the advancing goalkeeper on 70 minutes.
The second goal was important as Brighton pulled one back with 10 minutes to go with an excellent cross and header, which led to a tense finish as the home side chased an equaliser.
The Blades held on, deservedly, as on the reflection of the game had more chances and looked the more likely to score.
Coach Binnion said: "Jake Eastwood and Ioan Evans were superb throughout and deserve a special mention for their leadership and performance at the back. The group worked very hard and we had four u15/16s involved, which was great for their development."
Blades: Eastwood, Ishmail, Kedman, Calvert-Lewin, Whiteman, Evans, Coustrain, Partodikromo (Khan 72), Cockerline (Brown 76), De Girolamo, Ramsey (Wright 62).