The Brazilian will now face Frenchman Arnaud Clement, who beat his Davis Cup team-mate Sebastien Grosjean 6-3 7-6.
Federer was joined in the second round by Arnaud Clement of France who beat Dane Kristian Pless 7-5 6-3.
American Michael Russell upset fourth-seeded Raemon Sluiter 7-6 6-2 and number seven seed Arnaud Clement beat Oliver Gross 6-0 6-2.
Schuettler came into his first semi-final at Wimbledon just a day after completing an epic five-hour win over Arnaud Clement.
The American will next face France's Arnaud Clement , who led 6-3 5-5 when Argentina's Eduardo Schwank retired with an ankle injury.
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Sixth seed Cilic, the winner of ATP titles in Chennai and Zagreb already this year, defeated Arnaud Clement of France 6-2 6-4.
The previous longest match was at the French Open in 2004, when Fabrice Santoro beat Arnaud Clement after six hours and 35 minutes.
Spain's seventh seed Tommy Robredo lost to Argentine Jose Acasuso 2-6 6-3 6-4, and Croatian fourth seed Ivan Ljubicic beat France's Arnaud Clement 7-6 (8-6) 6-4.
Third seed Lleyton Hewitt was beaten 7-6 (7-1) 6-4 by Frenchman Arnaud Clement, who now meets Marat Safin after the Russian beat Wesley Moodie 7-6 (7-5) 7-6 (11-9).
Former world number eight Baghdatis came into the tournament in resurgent form, but was shocked 6-3 2-6 1-6 6-4 7-5 by France's Arnaud Clement at the Louis Armstrong Stadium.
Goffin stunned Czech 23rd seed Radek Stepanek in the first round proper, then beat more experienced opposition in veteran Frenchman Arnaud Clement -- playing his home tournament for the last time -- and Poland's Lukasz Kubot.
Djokovic will now face French qualifier Arnaud Clement, a 5-7 6-3 7-6 winner over German 16th seed Tommy Haas, with Del Potro to play Chilean 10th seed Fernando Gonzalez after he beat American John Isner 7-5 7-6.
"I played my best match here for sure, " said Nadal, who will have to wait to discover his next opponent as Arnaud Clement and Rainer Schuettler were forced to stop playing because of fading light when locked at one set all.
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