Orient posed the more frequent threats on goal during an even first half with midfielder Loick Pires seeing a cross land on Brighton's bar and soon afterwards let loose a left-foot drive which went over.
Seagulls defender Tommy Elphick was not far away with a header at a set piece and visiting midfielder Dean Cox and striker Glenn Murray both had shots comfortably held by home keeper Jamie Jones.
Orient midfielder Jason Demetriou and Patulea both saw ambitious second-half runs come to nothing and keeper Smith crucially smothered the ball at the feet of Pires.
The outstanding Cox weaved his way in on Orient's goal and had his shot blocked. The ball rebounded to striker Gary Hart, who fired wide. Patulea in turn saw his shot scrambled off the line and also headed against the bar before claiming the winner.