US Vice President Mike Pence was one of the special guests to address the service, held at Passion City Church in Atlanta, Georgia, and watched by over 75,000 people live on YouTube.
Pence described Zacharias as "the CS Lewis of our day" and a "gentle giant of the faith on whose shoulders so many of us leaned".
Close friends and family applauded as the Vice President drew parallels with the late Rev Billy Graham, who passed away in 2018.
"In the late Rev Billy Graham, it's been observed that God gave us the greatest evangelist of the 20th century. In Ravi Zacharias, God gave us the greatest Christian apologist of this century," he said.
He paid tribute to Zacharias as someone who spoke the truth but always did so "with kindness and a deep and abiding care for every person who would listen".
Recalling his last conversation with Zacharias from his hospital bed, Pence said the apologist had been more concerned for those struggling as a result of the coronavirus pandemic than he had been for himself.
"So I know Ravi would approve if, on this day, we also made a point to remember and pray for all who have endured heartbreak during these unprecedented times," the Vice-President said.
"So for his family, and families around America and around the world grieving the loss of a loved one, let's all pray that those who mourn would be comforted with the absolute assurance that he had, that the day will come when God will wipe away every tear from your eyes and theirs, and in every sense in these challenging times that He will heal our land."
Zacharias' daughter Naomi was tearful as she paid tribute to her father and his devotion to his family, calling him "the hero of our hearts".
"He was at home with those often overlooked, taken for granted or marginalised. A friend wrote that he could dine with kings and make a taxi driver feel like a king. If you were in front of him, he saw you," she said.
She added: "My father was ready to meet his Lord, but he fought as he did only because he didn't want to leave us."
Owing to coronavirus travel restrictions, Amy Orr-Ewing, Senior Vice-President of RZIM, the apologetics ministry founded by Zacharias, addressed the service from Oxford, England, by video link.
She said: "Ravi's had an enormous influence on me, on my life as an evangelist and an apologist, giving me opportunity first and foremost by inviting me to join his team when I was just in my early twenties myself, and that struck me as really amazing.
"I can't think of many other ministry leaders in 1998 who would have given a woman a chance to speak and preach and lead as Ravi did."
Louie Giglio, pastor of Passion City Church, added his own words of thanks to Zacharias, echoing Pence's words when he called him "a gentle giant of our faith in this generation".
In an emotional tribute, he described him as "one of the kindest, most anointed, most recognisable, most powerful voices in the global church" and "a rare treasure".
"Even though there was a massive calling on Ravi's life, he always saw people," he said.
"And he made you feel when you were around him like you were just hanging out with a normal guy ... He had this way of bringing people together."
Before his performance at the service, Christian rap artist Lecrae spoke about his friendship with Zacharias and how as a former atheist, he had sought out his apologetics videos to provide answers to his friends' "hard questions" about the Christian faith.
He said: "I used to find myself rapping in front of thousands of people travelling on the road, and leaving the stage to hurry back to my tour bus in order to devour his videos and his lectures ... and because of him, I now have these answers to hard questions."