Used mostly as a reliever, the Illinois native debuted in the big leagues with the Athletics in 1962 and spent time with the Angels, Braves, Red Sox, White Sox and Astros. Known as "The Silencer", Osinski was among the first to adopt a selected role as bullpen "closer", back before the job had an official title. Houston was the last stop in his eight big league seasons. He appeared in three games in 1970 and produced a 0-1 record and a 9.82 ERA. For his career, he posted a 29-28 mark with 18 saves and a 3.34 ERA.

Dan passed away on September 13, 2013 in Sun City, AZ at age 79.