Timo Werner put Chelsea ahead (28), nodding into the empty net from under the crossbar after Kai Havertz's chip had hit the woodwork, before Real rode their luck as the hosts missed four big chances to double their lead in the opening 20 minutes of the second period.
The hosts finally got their second to kill off the tie with five minutes remaining as Mason Mount stuck home substitute Christian Pulisic's centre at close range, capping off a fine display and marking an extraordinary turnaround at the club since Thomas Tuchel joined in January.
Chelsea will now play in their third Champions League final (2008 and 2012) in Istanbul on Saturday May 29, and have set up just the third all-English Champions League final after 2008 (Man Utd-Chelsea) and 2019 (Liverpool-Tottenham) as Manchester City look to complete a treble.
