The winger was introduced in the first half after Palace defender Patrick Van Aanholt had picked a knock after 30 minutes play.
With barely 15 minutes to end proceedings at the Selhurst Park, Schlupp scored a sensational having picked the ball from near the halfway line to run past Solanke and Billing.
The Black Stars player went on to beat Mepham who appeared to slow for the winger who shot past Ramsdale in post for Bournemouth.
This came barely just 30 seconds after Jordan Ayew had embarked on a similar run but had his final shot blocked.
The goal was enough as 10-man Palace picked all three points at home in English Premier League.
Jeffrey Schlupp has found the back of the net in his second consecutive games, having scored for Eagles in their 2-0 away victory against Burnley last Saturday.