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Title-holders Liverpool will face Diego Simeone's Atletico Madrid.
The 95th minute equaliser allowed second-placed Real to go level on 35 points with leaders Barcelona.
The draw leaves Barca still leading with 35 points from 16 games but Real Madrid, on 34, can take their place at the top if they win at Valencia on Sunday.
Chelsea, who needed a victory to make sure of qualification, had gone five Champions League games at Stamford Bridge without a victory, their longest such run at home in the competition.
Valencia, who missed a glut of chances, had taken the lead through Carlos Soler but goals from Mateo Kovacic and Christian Pulisic flipped the match on its head.
Two minutes into the match Chelsea captain Cesar Azpilicueta gave away a free kick and Tammy Abraham deflected Quincy Promes's whipped cross into his own net.
Barca's problems began when Luis Suarez was taken off injured and they collapsed in the second half, with Levante scoring with all of their first three shots on target.
La Liga champions Barcelona's long winning streak came to an abrupt halt when they suffered a shock 3-1 defeat away to Levante on Saturday.
Barcelona sailed back to the top of the table and trouble returned to Real Madrid after they endured their first La Liga defeat of the season at newly-promoted Real Mallorca.
Poland and Russia secured their places at Euro 2020 on Sunday with victories over North Macedonia and Cyprus respectively, while Germany and the Netherlands boosted their hopes of reaching the finals.