The 33-year-old Spanish striker scored one goal and set up another in a 2-1 second leg quarter-final victory for the Bundesliga side who now face Manchester United in the last four.
GEAR:Free printing andup to £20 off Champions League kits. Free delivery on orders over £50
Raul left Real Madrid last year after 16 trophy-rich seasons, including three Champions League titles, and he again proved he remains one of the most lethal strikers in Europe.
"These are the rewards for my constant hard work and my love for the game," a smiling Raul, the Champions League all-time top goalscorer who now has netted 71 times in Europe's premier club competition, told reporters.
"Now there will be two tough semi-finals with us against Manchester United and Real Madrid against Barcelona."
LIVE:Our interactive coverage as it happened
Raul has become a fan favourite in the former German coal-mining heartland - a far cry from cosmopolitan Madrid.
He killed off any hopes Inter had of getting back into the tie after their first-leg humiliation at the San Siro when he picked up a Jose Jurado cross and rounded Inter goalkeeper Julio Cesar to slot in the opening goal on the stroke of half-time.
"Raul scored one goal and set up the other for Beni Howedes," a beaming Schalke captain goalkeeper Manuel Neuer told reporters. "On Saturday the fans wanted Raul in the stands but Beni went. Today it is Raul's turn."
Schalke coach Ralf Rangnick, who has overseen four successive victories since he replaced Felix Magath last month, added: "This team played two great games against Inter and when you only allow two chances for the reigning champions then you understand how good this team worked."
Never before have the blue-whites played in the Champions League last four but thanks to Raul they now have every right to dream big when they face Manchester United.
It was never going to be a high-scoring game with Schalke careful to protect their first leg advantage but it was the perfect match for Raul.
Lurking for a quick break, the former Spain striker first threatened after a quarter of an hour with a header. He was on target just before the break, chasing down Jurado's cross to slot in before Thiago Motta levelled with a volley four minutes after the restart.
But the Spaniard then orchestrated their second win in two games against a largely toothless Inter, lobbing the ball forward over a static defence for Howedes to run on to and drill a low shot past Julio Cesar nine minutes from time.
The only time Raul looked unsure was when he was told to lead the celebrations
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
