Bayley, 29, defeated Ukraine's world number one Maksym Nikolenko 3-2 in the class 7 final.
Wilson, 21, overcame former world champion Richard Csejtey, from Slovakia, 3-2 in the class 8 final.
Another Briton, Martin Perry, lost to France's Bastien Grundeler in the class 6 semi-final, but took bronze.
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British Paralympic table tennis champion Will Bayley and Rio 2016 team-mate Ross Wilson both won singles gold at the PTT Bayreuth Open in Germany.