Bobby Zamora’s sixth goal in 14 games this season gave Brighton a deserved half-time lead. Paul Brooker released him when an Ipswich attack broke down deep inside the Brighton half.
The striker checked inside to beat Paul Gerrard with a 20-yard curler.
Zamora had almost put Brighton ahead in the sixth minute with an angled left-foot shot from Brooker's pass, which rebounded off the inside of a post.
Ipswich had to reshuffle when central defender John McGreal went off injured. Matt Holland dropped back into defence and they improved after the break once Joe Royle introduced Richard Naylor and top scorer Pablo Counago up front.
Michels Kuipers, Brighton's Dutch keeper, made a number of fine saves to keep them at bay. He twice stopped free-kicks from sub Darren Ambrose and tipped over a fierce long-range shot from Jamie Clapham.
But Kuipers could do nothing on 78 minutes when Northern Ireland international Magilton levelled with a well-struck shot from 25 yards.
Both sides could have won it in the closing stages, Nathan Jones chipped just over the bar for Brighton, then in stoppage time Kuipers deflected Counago’s effort from a tight angle into the sidenetting.
Brighton boss Coppell said: "We might easily have lost it in the last 20 minutes. Ipswich are a very good side, but my boys worked very hard in the second half to keep their heads above water."
Royle added: "I would not argue that Brighton deserved a point, it was possibly our worst performance since I have been here, but take nothing away from them."