Overkill toured for six months to promote Under the Influence, touring alongside thrash acts Nuclear Assault, M.O.D., Destruction and Testament. From October to December 1988, the band toured the United States with Slayer and Motörhead, followed by a European tour with Slayer and Nuclear Assault, which took place in January 1989.
Jason Anderson at AllMusic awarded Under the Influence three stars out of five, calling it "another confident, if unremarkable Overkill recording", while listing "Overkill III (Under the Influence)", "Shred", "Never Say Never" and "Hello from the Gutter" as highlights. The album reached No. 142 on the U.S. Billboard 200 and remained on that chart for thirteen weeks, making it Overkill's longest Billboard run. It is also their third highest-charting album to date, with over 300,000 copies sold worldwide as of 1997.