After ordination, Zielinski served as the parochial vicar at Immaculate Conception parish in Traverse City from 1996 to 1998. He then served as the pastor of St. Philip Neri parish in Empire and St. Rita-St. Joseph parish in Maple City. Zielinski was elected to the Presbyteral Council in 1999. Beginning in 2000, he also served as the pastor for administrative affairs of the Diocesan Mission to Hispanics. After the terrorist attacks of September 11, 2001, Bishop Cooney released Zielinski from the diocese to serve in the Archdiocese for the Military Services as an Air Force chaplain. He served as a chaplain at the Grand Forks Air Force Base in Grand Forks, North Dakota, from 2002 to 2003 and at RAF Mildenhall in Suffolk, England, from 2003 to 2005. He was next assigned to HQ Air Force Recruiting Service at Randolph Air Force Base in Schertz, Texas, followed by Cadet Chaplain at the United States Air Force Academy in Colorado Springs, Colorado, from 2009 to 2012. From 2012 to 2014 he served as chaplain at Eielson Air Force Base in Fairbanks, Alaska.