That's the tribute to the Late Chris Cornel by Ann Wilson and Jerry Cantrell.
Here's one of the songs performed by Bon Jovi
And a performance by the Cars
The Killers did a tribute to Tom Petty...
A performance by the Moody Blues
Dire Straits were also inducted, but since Mark Knopfler wasn't there they didn't perform. It was also weird that noone inducted the band. John Illsley, bassist for Dire Straits was the one who inducted the band.
HBO will air highlights from the R&R Hall of Fame induction ceremony on May 5th.