The 30-year-old was troubled at times by Szpilka, who had lost just one of his 21 outings as a professional, but the American ended the contest in emphatic fashion in the ninth round.
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As Szpilka lunged forward, he was caught with a thudding right hand by Wilder, bringing an abrupt halt to the fight with the Pole unconscious on the canvas.
The victory sees Wilder extend his unbeaten record to 36 victories and sets up a clash with mandatory challenger Alexander Povetkin.
After the fight, Wilder was involved in a verbal confrontation with Tyson Fury, the WBA and WBO champion, with a unification showdown likely should Wilder beat Povetkin and Fury get the better of Wladimir Klitschko in their rematch, which will take place in the spring.