Cologne defender Rafael Czichos gave the visitors a first-half lead, but Hoppe equalised before the hour mark.
Cologne snatched a late win when Jan Thielmann fired past Schalke goalkeeper Ralf Faehrmann in injury time.
The win lifted Cologne out of the relegation play-off place to 15th, while Schalke remain behind second-bottom Mainz on goal difference.
Hoppe became the first American to score a Bundesliga hat-trick in the 4-0 thrashing of Hoffenheim 10 days ago which ended Schalke's 30-match winless run in the league, before also netting in Sunday's 3-1 defeat at Eintracht Frankfurt.
Schalke next host league leaders Bayern Munich on Sunday having been thrashed 8-0 by the European champions at the Allianz Arena on the opening day of the season.
The Royal Blues' new signing Klaas-Jan Huntelaar missed Wednesday's game with a calf strain after rejoining on Tuesday following two years with Ajax.
Cologne ended a miserable five-match goalless run in the league when Czichos headed home a deflected cross with half an hour played.
Cologne nearly went 2-0 up just after the break when Schalke midfielder Benjamin Stambouli clipped his own post with an attempted clearance.
The hosts drew level when Hoppe pounced on a loose ball in the area, before Thielmann's late winner.