It meant Didier Drogba's return to Stamford Bridge ended in defeat as the Blues overcame the Turkish champions 2-0. Jose Mourinho warned of a dangerous tie poised 1-1 after the first leg in Istanbul three weeks ago, but four minutes into the second leg his side regained the advantage before advancing into Friday's last-eight draw with ease.
Drogba, scorer of 157 goals in 341 appearances over eight years for the Blues, including the decisive penalty in the 2012 European Cup win, was expected to be the main protagonist of the contest.
But it was another 30-something African striker who found the net with the first attack as, for once, the Ivorian faded into the background on the big occasion, with Eden Hazard the outstanding forward on display.
Eto'o, a Champions League winner with Barcelona and Mourinho's Inter Milan, justified his return to the starting line-up with his tenth of the season - all of which have come at home - after breaching the offside trap to latch on to Oscar's pass and convert with a shot which squirmed under Fernando Muslera's right hand.
Frank Lampard's free-kick was volleyed narrowly over by John Terry and a Drogba set-piece from a similar distance at the other end was so far over it hit the banner bearing his name. Eden Hazard and Eto'o combined to set up a chance for Willian, who could only weakly direct the ball straight at Muslera, but soon Chelsea had their second. Lampard and Terry combined at another set-piece and this time the captain's header from a corner was saved, with Cahill following up to thrash the ball into the net.
Chelsea set about trying to add to their lead and went close in the opening skirmishes of the second period. Oscar was unable to test Muslera after a mesmerising Hazard run before the Galatasaray goalkeeper saved from Willian and Oscar shot wide after cutting in from the left.
Lampard headed straight at Muslera as Chelsea continued to search for a third, before Drogba was booked for tugging back Cesar Azpilicueta. Torres, on for Eto'o, was teed-up by Hazard and denied by the visiting goalkeeper as Galatasaray and Drogba were eliminated.
Real reach cloud nine
Real Madrid unsurprisingly booked their place in the quarter-finals of the Champions League after wrapping up an emphatic aggregate victory over Schalke - but the Spanish side's night was soured by a potentially serious injury to talented young forward Jese.
A brace from Cristiano Ronaldo - his 40th and 41st goals of the season - and one for Alvaro Morata sealed a 3-1 victory on the night as Madrid dotted the i's and crossed the t's on a last-16 tie that was as good as over in the wake of their 6-1 victory in the first leg three weeks ago.
Tim Hoogland's heavily deflected strike was all Schalke had to show from their trip to Madrid, although Jens Keller's men were at least spared a repeat of the abject drubbing they suffered on home turf last month.
Jese reportedly suffering a suspected anterior cruciate ligament injury in an innocuous tussle with Sead Kolasinac inside two minutes. The unfortunate Spain Under-21 international was replaced by Gareth Bale and the Wales international did not need long to make a telling impact.
With 22 minutes gone, good work by prolific Spain Under-21 striker Morata created the chance for Bale to work a yard of space on the right and drill in a low cross that Ronaldo turned home first time to take him past the 40-goal milestone for a fourth successive season.
Despite their mauling three weeks ago Schalke were a good match for Madrid throughout the half and deservedly pulled one back after half an hour when Hoogland was allowed to advance through the midfield before rifling an effort that took a massive deflection of Ramos to wrong-foot Casillas.
Ralf Fahrmann did all he could to maintain parity, but Madrid's goal threat was ever-present. It came as no surprise when they regained the lead on the night with 74 minutes on the clock, Ronaldo collecting the ball in midfield and running powerfully at the back-pedalling home defence before drilling a low effort inside Fahrmann's near post.
Ronaldo could and should have been celebrating a hat-trick two minutes later when he fired against the bar with the goal at his mercy after Fahrmann had saved Morata's initial effort, but although Ronaldo had been thwarted the danger had not passed and Bale was able to steer the ball back towards the waiting Morata, who clinically slotted home.