Inter were always up against it after suffering a crushing 5-2 first-leg defeat on home soil, but a memorable fightback never looked to be on the cards as they produced a tepid first-half produced at the Veltins-Arena.
It was only with 10 minutes to go in the half that the Italian champions finally managed to trouble Manuel Neuer in the Schalke goal, and the Germany international responded in style with a fingertip save to deny Dejan Stefanovic.
And their defence was all but over when Raul struck on the stroke of half-time, racing onto a Jose Manuel Jurado through-ball before rounding Julio Cesar to net record 71st goal in the Europe’s premier club competition.
Inter pulled one back five minutes into the second half when Wesley Sneijder’s cross was met by Lucio and Thiago Motta diverted the ball into the net, but Benedikt Howedes, who earlier had a ‘goal’ incorrectly ruled out for offside, won it for Schalke with nine minutes remaining.
The German side now face a two-legged semi-final showdown with English Premier League leaders Manchester United.