Assembly and method for extracting fluids, preferably crude oil, from a drilled well within a geological formation by means of reciprocating pumping with hollow sucker rods. The assembly includes: a) a stationary bottom set that attached to the casing at the desired depth and providing the rod pump anchoring system; b) a reciprocating axial movement rod pump having an anchoring system and a centralizer; c) a centralized hollow rod string extending within the well, which is connected to the mobile member of the pump; d) a hollow polished rod connected to the hollow rod string and linked to a system that imparts the reciprocating axial movement to the pump; e) a production bridge connecting the polished rod to the driving tubing through rotating joints, and f) a rigid head that provides a venting exit of the annular space formed between the string and the casing.