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Having won the quarterfinal first-leg 5-2 at Inter's San Siro stadium last week, the second-leg back in Germany was always going to be a formality.
Spain legend Raul opened the scoring on the stroke of half-time to extend his record Champions League tally, with Inter midfielder Thiago Motta levelling minutes after the restart.
Defender Benedikt Hoewedes put the matter beyond doubt with a late winner, rubber-stamping Schalke's first ever appearance in the semifinals of Europe's premier club event.
Inter came to Gelsenkirchen facing a near-impossible task of needing to score four goals to go through to the semifinals to face Premier League giants United.
In the end, ex-Real Madrid star Raul, one of the scorers at the San Siro, put the Royal Blues ahead before Motta levelled for the guests before Hoewdes' winner.
Schalke will now host United at their Veltins Arena stadium on April 26 in the first-leg of the semifinal and Manchester manager Sir Alex Ferguson was in Gelsenkirchen to watch the Royal Blues' quarterfinal.
The hosts took the lead just before the half-time break when Spanish midfielder Jose Manuel Jurado split the Inter defence with a perfectly-timed pass into the path of compatriot Raul.
The Spain veteran needed no second invitation to round Inter goalkeeper Julio Cesar and slot his shot into an empty net in the 45th minute.
It was the Spaniard's 71st Champions League goal, his fifth goal of this European campaign and the 33-year-old's 18th since joining Schalke from Real at the start of the season.
It put Schalke up 6-2 on aggregate and effectively killed off any flicker of hope the Italians had.
The guests levelled the scores when Motta was left unmarked from a corner and headed home on 49 minutes.
Schalke looked to have regained the lead on the hour mark only for Hoewedes' header to be ruled off-side, but the defender scored the winner when he ran onto a long pass from Raul to drill his shot past Julio Cesar in the 81st minute.
