Has a cover band opened for the band they do covers of? I have never heard of it happening although it might be daring for the both of them.
I found this one:[
The Australian Pink Floyd played at David Gilmour’s 50th birthday party.
I don’t know if this counts but I saw the Bob Dylan Rolling Thunder revue in the mid 1970s which had people such as Roger McQuinn (Byrds) and Joan Baez appearing before Zimmerman came out. Both had done a number of Dylan covers but didn’t that night. The only song McQuinn did was his own “Chestnut Mare” and Baez did “Diamonds and Rust” and a couple others.
I remember some benefit concert on MTV in the 1980s when two people did “Everytime You go Away”-Paul Young and maybe Alison Moyet. In both cases it was still a shitty song.
Ex-Lion Tamers (With a young Jim DeRogatis) openedfor Wire on tour back in 1987.
In the film “A Mighty Wind” (one of my all-time favorites), The New Mainstreet Singers did a song which was a cover of The Folksmens’ hit, “Never Did No Wanderin’” causing an argument among the group if they should go ahead and do their own song anyway. This was a case of the cover group sounding better than the originals.
If you are old enough to remember the “Hootenanny” shows, I highly recommend this film! 
Q
A couple of sort-ofs:
When I saw Sparks circa 1982, Ron and Russell Mael opened for themselves in the persona of a lounge act, doing easy listening versions of Sparks songs. I don’t remember what they called themselves, and I think they reversed roles: Ron singing and Russell playing the keyboard.
I saw a Van Morrison set where the first couple of songs were Van Morrison numbers sung by backing singer Brian Kennedy before Morrison himself appeared.