Ipswich have extended their unbeaten run to four games and consigned Brighton to their fourth defeat in five games.
The Tractor Boys dominated the first half but failed to break through Brighton's rearguard, and it was the visitors who surprisingly took the lead eight minutes into the second half.
New Spanish signing Vicente ran from the halfway line before cutting inside and curling a shot into the far corner.
The Seagulls' lead did not last long however, as Ipswich equalised six minutes later when striker Michael Chopra scored an effort similar to that of Vicente's.
The points were secured when Chopra scored another similar effort by cutting in and firing past Kasper Ankergren into the Seagulls' net.
Ipswich move up to tenth position and will travel to Cardiff after next weekend's international break while Brighton, who remain fifth despite the defeat, host Hull on Saturday, October 15.