Despite going a goal down early on, Ipswich kept playing some neat passing football, and virtually had the match sewn up by half time, by which time they led 3-1.
Pablo Counago had seen one firm shot well saved by Andy Petterson, and then fired wide before Brighton claimed a surprise lead.
Andy Marshall missed Paul Watson's curling free-kick and Brighton debutant Dean Hammond looped a shot into the unguarded net after eight minutes.
Town levelled after 13 minutes when Darren Bent sidefooted home a Jamie Clapham cross and then after 22 minutes Clapham's pass sent Counago racing through to beat his man and curl home his seventh of the season.
Richard Carpenter's tremendous free-kick for the visitors came back off the bar with Marshall beaten before Town grabbed a third on the stroke of half time.
Darren Ambrose let fly from 25 yards with a shot which bounced down off the bar and over the line, which was well spotted by the assistant referee.
The second half was understandably less dramatic, with Ipswich happy to defend their two-goal advantage.
Brighton could have made them pay though as first sub Chris McPhee had a low shot blocked by Marshall, before Paul Brooker twice fired narrowly off target.
By now Ipswich had taken off scorers Counago and Ambrose, replacing them with Finidi George and Marcus Bent with the latter looking particularly lively.
He volleyed wide from a Jim Magilton cross before a superb diving save from Petterson kept out his low curling drive.
His best moment though came in the final minute when his angled chip came back off the far post, with Bent first to the ball, but he shot over the open net.
This win eases the pressure on under-fire Town boss George Burley but will only increase the fears of his Brighton counterpart, Martin Hinshelwood, for his own job