The two-time defending champions beat the Indiana Pacers 117-92 to ensure that they progress with a 4-2 series victory over their Eastern Conference rivals.
The forward told reporters: "I'm blessed. Very blessed. Very humbled. And we won't take this opportunity for granted. It's an unbelievable franchise, it's an unbelievable group.
"And we know we still have work to do, but we won't take this for granted. We're going to four straight Finals and we will never take this for granted."
The Heat will face either the San Antonio Spurs or the Oklahoma City Thunder in the finals, which get underway next week.