Eubank Jr, the IBO champion, maintained his momentum from a strong start when the Turk was almost felled by a right upper cut in the opening round, dropping to his knee before taking a standing count.
Yildirim, who weighed in at the 12st weight limit and was previously undefeated from 16 professional fights with 10 knockouts, recovered for the second, when he started to find range with his jab.
However, Eubank Jr stepped things up again in round three. Yildirim was left exposed by a flurry of rapid punches from the Briton before being put down by a fierce left hook which prompted the referee to immediately step in after one minute and 58 seconds, with the Turk still sprawled on the canvas, and call a halt to the one-sided contest.
Eubank Jnr, who had fought outside the United Kingdom only once previously, will now take on the winner of next week’s fight between Jamie Cox and George Groves.
“I am here to dominate this tournament. I am sending a message out there that I am coming,” he said at ringside, broadcast on ITV Box Office.
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Despite the superb show from the British boxer, who should now be in line to meet David Benavidez for the WBC super-middleweight title, there had earlier been some crowd trouble at the Hanns-Martin-Schleyer Halle ahead of the main bout.
Pictures published online and social media from the event showed fighting between rival groups, with chairs being thrown and some men left blooded.