A match which began with Internazionale scoring one of the great Champions League goals ended with their Champions League ambitions all but dead as Schalke twice came from behind in the San Siro to claim a commanding advantage in their quarter-final.
Dejan Stankovic needed just 25 seconds to volley his side into the lead with a stunning hit from the centre circle, but Joel Matip levelled, just as Edu did before half-time after Diego Milito restored Inter's lead.
It was all downhill for the Italian champions after the break as Raul netted for Schalke, Andrea Ranocchia scored an own goal and Cristian Chivu picked up his second red card in four days, before Edu notched again to round off a miserable night.
It all looked so promising for Inter, who were coming off a 3-0 defeat against derby rivals AC Milan, as they immediately took the lead in stunning fashion.
Manuel Neuer advanced out of his area under pressure from Milito and headed clear.
He got good distance but the ball went straight to Stankovic in the centre circle, who showed great technique and power to volley first time over the defence, over Neuer and over the line.
Raul had two good chances to equalise inside the next five minutes, heading first wide and then straight at Julio Cesar.
At the other end, Milito did well down the left beat two defenders and get a cross in, but Wesley Sneijder could not keep his header down.
But Schalke were level in the 17th minute.
Kyriakos Papadopoulos was left completely unmarked at the far post from Jefferson Farfan's corner and, though his header was straight at Cesar, the ball broke to Matip, who hammered home.
Inter appealed for a penalty when Milito went down under pressure from Atsuto Uchida when through on goal, but referee Martin Atkinson decided there was no foul.
Manuel Jurado then shot straight at Cesar, before at the other end Eto'o had a goal chalked off for offside to bring a hectic opening 20 minutes to a close.
Stankovic's eventful evening - he was also booked - came to a premature end when he succumbed to injury after 24 minutes and was replaced by Houssine Kharja.
But Inter did not let the change knock them out of their stride and they were ahead nine minutes later.
A neat move involving Milito and Javier Zanetti saw Sneijder cross to Esteban Cambiasso at the far post.
Cambiasso headed back across goal to Milito, who, having stayed just onside, had a simple task to finish from close range.
They could not hang onto their lead until half-time, though, as Edu drew Schalke level, following up to finish from a narrow angle after Cesar had done well to save his initial deflected shot.
Inter should have had a goal a minute into the second half as well, as Sneijder picked out Milito, who controlled well but sent a left-footed shot inches wide of the left post.
Two minutes later, Sneijder played in Eto'o, who turned Benedikt Howedes before seeing his shot brilliantly saved by Neuer.
But it was Schalke who took the lead in the 53rd minute as Raul claimed his 70th Champions League goal, finishing low past Cesar after good work by Farfan.
And it got worse for Inter four minutes later when Ranocchia slid in under no pressure and diverted Jurado's low cross into his own net.
Eto'o had a glorious chance to pull one back moments later but he dragged a left-foot shot wide from 10 yards.
Chivu was shown a second yellow, having also been sent off in the Milan derby, for a challenge on Edu in the 62nd minute which the Brazilian made the most of. They almost paid the price three minutes later when Jurado crashed a shot against the post.
Farfan's 75th-minute shot was saved by Cesar and his follow-up effort turned against the post by Ranocchia, but moments later the ball broke to Edu, who turned Ranocchia and curled the ball past the despairing goalkeeper.
A shellshocked Inter rarely threatened thereafter and they will have a mountain to climb in Gelsenkirchen next week.