Trailing by three goals at half-time, a Jefferson Farfan strike was scant consolation as Jens Keller's men bowed out in front of 51,000 fans at the Arena AufSchalke.
Kai Herdling, scorer of a spectacular goal in the Bundesliga at the weekend, set Hoffenheim on their way to victory in the 21st minute, with Kevin Volland and Roberto Firmino netting twice in three minutes to leave boos from the home team echoing in the ears of the Schalke players as they left the field at the interval.
Schalke tried to respond in the second half, but a Farfan effort midway though was all they had to show for a disappointing night.
There was no such disappointment for Borussia Dortmund, who remained on course for a second final appearance in three seasons with a 2-0 win at third division Saarbrucken.
Coach Jurgen Klopp made numerous changes to his normal starting XI, but he could still rely on Jonas Hofmann and Julian Schieber to score the goals which took the Westphalians through to the last eight.
Robert Lewandowski stayed on the bench while goalkeeper Mitchell Langerak continued his flawless record of having won every single game he has played for the club on German soil.
Elsewhere, Hamburg came through a tricky tie against 2.Bundesliga leaders Cologne, with substitute Ivo Ilicevic grabbing an 85th-minute at the HSV-Arena after Maximilian Beister's opener had been cancelled out by Adam Matuschyk.
Finally, Kaiserslautern ensured there will be at least one second-tier side in the quarter-finals as they eased past fellow 2.Bundesliga outfit Union Berlin 3-0.