Despite hitting back to gain a draw, wins elsewhere for Wolves and Nottingham Forest leave Town with a mountain to climb.
Pablo Counago chipped an early chance over the bar before putting Matt Holland through but Dave Beasant easily gathered his weak drive.
Holland sent a header and shot wide before Town went ahead on 20 minutes, Marcus Bent slotting Danny Cullip's weak back-pass beyond Beasant.
Holland fired two more long-range shots over before Counago's filcked effort was held by Beasant.
Little had been seen of Brighton as an attacking force, but they should have levelled on 39 minutes when the unmarked Dean Blackwell sent a header over from a Richard Carpenter corner.
Carpenter forced the first save out of Andy Marshall on 48 minutes, and then both Gary Hart and Carpenter fired off target as Brighton increased the pressure.
It was no surprise when they equalised on 66 minutes, when Tony Rougier's header from a Hart cross hit the bar and rebounded in off the unlucky Marshall.
Town should have regained the lead two minutes later when Chris Makin was fouled by Carpenter but substitute Darren Bent blasted the penalty over.
Darren Bent and Fabian Wilnis both saw efforts saved by Beasant before Brighton went in front nine minutes from time, Rougier tapping in after great work down the left wing by Paul Brooker.
Ipswich hit back just two minutes later, with Martijn Reuser lashing a 25-yard drive past Beasant from substitute Tommy Miller's lay- off.
Despite four added minutes neither side threatened a winner, with Brighton happy to play for a point.
However, Ipswich now facing another cash-strapped season in Nationwide Division One and maybe more transfers out next week.