Peter Beardsley orchestrated Fulham's 1-0 victory with a vintage display, as Palmer's blunder handed Fulham their goal in the 10th minute.
Palmer's night to forget began when he clumsily trod on the ball and handed Beardsley the chance to run clear and set up the German striker, Dirk Lehmann, who made no mistake to give the Second Division side the lead on the night and a 2-1 aggregate advantage.
Saints' former England midfielder, playing in the centre of defence, was booked 30 seconds later following a tussle in the Fulham penalty area. Then the referee, Paul Durkin, had no option but to dismiss Palmer in the 36th minute when he was guilty of a dreadful late challenge on Lehmann.
Having been reduced to 10 men, Saints could find no way back as they suffered their eighth consecutive match without victory in a dismal start to their season. It could have been even worse had Wayne Collins found the target with a header in the 54th minute from a Steve Hayward corner.
Hayward also tested the Southampton goalkeeper, Paul Jones, with a scorching left-foot shot from 20 yards. The former Saints goalkeeper, Maik Taylor, did not have a save to make on his return to The Dell, as Kevin Keegan's side progressed safely into the third round.
"We should have beaten the Saints at Craven Cottage," Keggan said, "but it's even more special coming here and beating them at The Dell. Not many clubs come here and win."
The Chinese international, Fan Zhiyi, scored his first goal for Crystal Palace, but Terry Venables' men bowed out 4-2 on aggregate against their First Division, rivals Bury.
Palace had high hopes of a comeback when Clinton Morrison opened the scoring as they tried to overhaul a 3-0 first-leg deficit. The former Eagles trainee launched his side's fightback with an eighth-minute strike - only to score an own goal 17 minutes later to make it 4-1 to Bury.
Fan scored with 13 minutes remaining, but by then it was too late for the Selhurst Park side, who lost 4-2 on aggregate.
Barnsley drew 1-1 with Reading at the Madejski Stadium to preserve their three-goal advantage from the first leg at Oakwell, and go through by a 4-1 aggregate margin. Ashley Ward scored for the Tykes and Darren Caskey equalised for the home side, but it will be Barnsley in the hat for Saturday's third-round draw.Reuse content