Cowboys receiver Terrance Williams was challenged to a sprint outside XTC Cabaret in Dallas Monday morning ... and TMZ Sports has the crazy footage!!

Here's what we know -- T-Will was leaving the strip club around 5 AM Monday after a birthday party for a pal when his best friend started feeling all Usain Bolt and asked him to race!

Not only was Williams down for a little sprint action, he REALLY got into it -- ripping his shoes and shirt off to get comfortable.

Williams tells TMZ Sports the whole thing was in good fun -- and even though he SMOKED his pal, there was nothing but love between everyone.