We propose a new collaborative clock offset estimation scheme between two nodes in the Internet using independent one-way offset estimations. Our proposal (different than current schemes in the literature) is intended to provide a fast and accurate clock offset estimation in approximately [Round-Trip Time (RTT)+40]ms. The scheme sends a group of 5 probes in the the forward and reverse paths, and models the One-way Transit Time (OTT) by a Gamma distribution (with parameters adapted to actual path condition) to estimate the minimum distribution value (or long-term minimum OTT value). End nodes exchange their corresponding minimum distribution values to get an improved final clock offset estimate, which takes into account the network path asymmetries. We show that our scheme provides a faster clock offset estimation with lower RMSE and superior stability than NTP and current NTP-like state of the art methodologies in the literature.