Anthology series (1980s?) Invasion from another planet similar to TZ "Will the Real Martian Please Stand Up?"

I thought this was "Amazing Stories," but maybe not.  Anyway, it was somewhat light-hearted, and I'm thinking the original invasion was broadcast by radio (like "War of the Worlds), and at the end, one of the characters makes the comment "Now for the invasion from Jupiter! (or Saturn)"  Could have sworn it was Harvey Korman who did the Barney Phillips punch line, but I didn't see him in any anthology in that time frame.