A bit hard to tell, as there was a lot going on in firearms and ammunition design in that era. But I think the first successful auto pistol in terms of actual manufacture and sale (not experimental or test models) was the Borchardt, which was patented in 1893 and was in production at least two years before the Mauser C96.
The earliest auto pistols I can find in the books date to 1892. These are the Kromar, the Schwarzlose, and the Schoenberger-Laumann. The Kromar and Schoenberger-Laumann, along with the Salvator-Dormus of 1894 were entered in Austrian trials in 1894; none were found acceptable. Mannlicher and Bergman were also early pioneers (though the Bergmann No. 5 pictured above dates to 1897). Browning's first pistol was gas operated and dates to 1895, although it was not patented until 1897, when Browning patented a group of pistols including a rotating barrel design, the blowback that became the FN Model 1900, and the double link locking system that evolved into the Model 1911.
Jim