Schlupp, who was on the scoresheet during Saturday’s 2-0 victory at Burnley, grabbed the only goal of the match with 14 minutes remaining as Roy Hodgson’s team once again showed great character.
After a low-key opening to the match, during which James McArthur hit a volley wide for the home team, Palace were reduced to 10 men in the 19th minute when Mamadou Sakho, who had replaced Scott Dann in the starting line-up, was sent off for a high challenge on Adam Smith.
The Cherries, who made four changes to the team that lost 3-2 at Tottenham on Saturday with Smith, Chris Mepham, Phil Billing and Harry Wilson all coming into the side, created their first opening shortly afterwards but Mepham’s shot was straight at Vicente Guaita.
Hodgson’s side suffered another blow 10 minutes after the red card when Patrick van Aanholt picked up a hamstring injury and had to be replaced by Schlupp.
Bournemouth midfielder Billing sidefooted a shot straight at Guaita just before the break while at the start of the second period Dominic Solanke could not quite latch on to Wilson’s excellent right-footed cross.
Palace continued to look dangerous despite only having 10 men and Jordan Ayew headed a half-chance wide from a set-piece while Wilfried Zaha had a penalty appeal ignored after he went down under Mepham’s challenge.
Eddie Howe’s side struggled to create many clear-cut openings throughout the encounter and they fell behind in the 76th minute when Schlupp beat two men before firing past Aaron Ramsdale who looked as though he should have done better.
Guaita made a good save to keep Jefferson Lerma’s late effort out but Bournemouth did not deserve anything from the match after producing a lack-lustre performance.