The German giants had not claimed a league victory since January 2020 heading into Saturday's home game against Hoffenheim.
Failure to win again would have seen Schalke equal Tasmania Berlin's record stretch of 31 Bundesliga matches without success from 1965-66.
However, an inspired outing from 19-year-old Hoppe set up a 4-0 triumph at the Veltins-Arena, ending that miserable streak and moving Schalke off the foot of the table.
The American had never previously netted a senior goal but repaid the faith shown in him by Christian Gross, Schalke's fourth coach of the season.
Hoppe's opener came in contentious circumstances three minutes before half-time, with a handball on the edge of the hosts' box unpunished before a rapid counter saw Amine Harit send the forward through to lift a superb finish over Oliver Baumann.
Harit created all three Hoppe goals, although the scorer did the majority of the heavy lifting on each occasion, rounding Baumann for the second in the 57th minute and beating the goalkeeper with another dinked effort six minutes later to complete his treble - the first by an American in the Bundesliga.
The goal Harit deserved completed the scoring 11 minutes from time, drilled beyond Baumann at his near post to end Schalke's drought in spectacular fashion.
Having avoided a share of Tasmania's unwanted piece of history, Schalke are above Mainz and now only three points away from the relegation play-off place, although 16th-placed Arminia Bielefeld play on Sunday.
Meanwhile, Schalke's clean sheet left opponents Hoffenheim as the only side yet to record a shutout in the top flight this term.