Griffey gave away the hat he wore on stage during his induction to Tyler and Kristin Marino, who lost their NYC firefighter father on 9-11.
Griffey, who was their father's favorite player, hit a home run in 2001 in honor of the firefighter at the request of his widow, Katrina Marino. Griffey later met the Marino children when the Reds played the Mets in New York in July 2002.
Piazza's entry also brought back memories of 9-11's aftermath.
Piazza's two-run homer in the eighth inning at Shea Stadium lifted the Mets to a 3-2 victory over the Braves in the first sporting event played in New York after the terror attacks.
Piazza paid tribute to that moment in his induction ceremony.
"To witness the darkest evil of the human heart ... will be forever burned in my soul," Piazza said. "But from tragedy and sorrow came bravery, love, compassion, character and eventual healing.
"Many of you give me praise for the two-run home run in the first game back on Sept. 21st, but the true praise belongs to police, firefighters, first responders that knew that they were going to die, but went forward anyway. I pray that we never forget their sacrifice."
Information from The Associated Press was used in this report.