Silgado, 27, looked the better fighter in the first three rounds before the 33-year-old Russian south-paw regained control midway through round four.
Lebedev threw a powerful left hook that stunned Silgado, then unleashed a devastating left uppercut to the chin of his opponent, knocking him out with less than a minute remaining to the delight of the partisan home crowd at Moscow's Crocus City Hall.
"I didn't know much about my opponent, therefore I was patient, I was taking my time," Lebedev told reporters.
"I knew if I hit him with my best shot I could hurt him."
It was the first title defense for Lebedev, who improved his record to 25 wins, including 19 by knockout, and one defeat - a controversial points decision against German Marco Huck in a title bout in 2010.
In October, the WBA stripped Panamanian champion Guillermo Jones of his title for refusing to fight Lebedev and awarded it to the Russian.
Among others, Lebedev knocked out former multiple world champion Roy Jones Jr. in a light-heavyweight non-title bout last year.
For Silgado it was his first defeat in 24 professional fights.
(Reporting by Gennady Fyodorov, editing by Ed Osmond)