The Seagulls peppered Lewis Price's goal before Dean Hammond fired in Colin Kazim-Richards' right-wing cross.
Home midfielder Charlie Oatway went off with a neck injury before Ipswich's Sam Parkin scored off Fabian Wilnis' cross.
Parkin crashed another header on to the crossbar and Leon Knight rattled the woodwork but neither team could find a way past two outstanding goalkeepers.
Ipswich manager Joe Royle
"Brighton were far better before the break but we then passed the ball and shaded the match. "Sam Parkin has done fine for us. He has scored all his goals so far this season away from home and that is a shame for our home supporters.
"It was a great goal and he just needs the type of encouragement he received in this game."
Brighton: Henderson, Hart, McShane (Robinson 74), Butters, Reid, Carole, Oatway (Nicolas 33), Hammond, Frutos (El-Abd 61), Knight, Kazim-Richards.
Subs Not Used: Turienzo, Chaigneau.
Booked: Knight, Nicolas.
Goals: Hammond 15.
Ipswich: Price, Sito, De Vos, Naylor, Wilnis, Currie (McEveley 88), Proudlock (McDonald 54), Juan, Richards (Magilton 32), Bowditch, Parkin.
Subs Not Used: Peters, Supple.
Booked: Juan.
Goals: Parkin 39.
Att: 6,867
Ref: R Beeby (Northamptonshire).
MMIX
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