Alvarez, 53, a husband and father of three sons, died in hospice care from cancer on Saturday. His death came weeks after he testified before Congress to urge lawmakers to extend the victim compensation fund that many first responders depend on to pay their medical bills.
Alvarez was born in Cuba and was a toddler when his family moved to New York. He signed up for the Marines Corps when he was 18. He went on to join New York's police department in 1990 and became a highly decorated officer, working undercover and on the bomb squad.
"Before he came an American hero, he was mine," his eldest son, David Alvarez, said at the service. "The one above all I wanted to make proud."
"Growing up I'd be told by family members that I was just like my dad. I laugh like him, I smile like him, I walk like him, I'm quiet and stubborn like he was," he said. "I always took it as compliments... because I always looked up to my dad, always wanted to be like him."
After the attacks on the World Trade Center on Sept. 11, 2001, Luis Alvarez worked at Ground Zero, cleaning the rubble and waste left at the site. He was diagnosed with cancer several years ago and underwent dozens of rounds of chemotherapy.
On June 11, Alvarez joined former "Daily Show" host Jon Stewart, and dozens of 9/11 first responders to demand that Congress fully fund the 9/11 Victim Compensation Fund that was set up for police, firefighters and others who worked at Ground Zero.
"I did not want to be anywhere else but Ground Zero," Luis Alvarez told Congress.
"This fund is not a ticket to paradise," he said of the 9/11 Victim Compensation Fund. "It's there to provide to our families when we aren't there."
Luis Alvarez "emphasized with blunt grace that future families stand not only to experience the stress of fighting these terrible illnesses but that their struggles would be compounded by the unconscionable financial burden of trying to fund their healthcare," NYPD Commissioner James O'Neill said at Wednesday's service, which was also attended by Stewart.
The ill first responder "just wanted to do what's right and he desperately wanted others -- in particular those in positions of great power -- to follow suit," the commissioner said.
After his cancer diagnoses, he showed "tenacity and resilience that even surprised his oncology team," said his sister, Ida Lugo. "Nevertheless, chemo became his prison, his jail. Often isolating him from the world, too sick to engage."
"He wanted to urge our government to do the right thing," Lugo said. "It became my brother's dying wish, the legacy he wanted to leave that the bill protecting the Victim Compensation Fund be passed."
Twenty-three NYPD officers died on 9/11. As of Wednesday, 222 NYPD officers, including Luis Alvareaz, have died from 9/11 related illnesses, O'Neill said.
A bill to extend the Victim Compensation Fund passed a House committee in June and is awaiting a full House vote before it is taken up by the Senate.
ABC News' Erica King contributed to this report.