The 14th-seeded Isner, who reached the Miami Open semifinals in 2015, never faced a break point in the match. He made an impressive 73 percent of his first serves to take down Cilic.
"I was in a very good serving rhythm today," Isner said. "I felt that really from my opening serve, the whole match that I knew it was going to be a good serving day.
"When I serve like that, I'm certainly tough to beat," Isner added.
The key to Isner's victory in the match came when he won all seven points in the first-set tiebreaker.
"In the blink of an eye I was up 5-0 and I was able to win it 7-0, a very good tiebreaker, because prior to that the match was a bit choppy," Isner said. "The wind was of course tricky, and it was pretty ugly, but I played a very good tiebreaker."
The departure of Cilic, the 2014 U.S. Open champion and Australian Open finalist in January, leaves fourth-seeded Alexander Zverev of Germany as the highest seed remaining in the draw.
"I get too much love from them," Del Potro said of the fans. "I am excited to keep winning, to stay longer and play in this tournament.
"I know it will be the last time here in Key Biscayne, and I think playing here they make a special tournament for all the South American players, basically me," he added, smiling.