Isner had three aces in the tiebreaker, including a 125 mph shot at set point. His other aces were clocked at 137 and 138 mph.
Harrison broke Isner's powerful serve in the ninth game of the second set, but Isner broke right back and took the victory at the third match point.
Sixth-seeded Fernando Verdasco of Spain broke a string of three straight opening-round losses with a 7-6 (5), 6-2 victory over Steve Johnson of the United States.
"He came up with a couple of good shots in that last game and I missed some by fractions," Harrison said. "I'm a half inch from hitting my spots perfectly. At that point, you can't keep analyzing it. Sometimes the fractions go your way and sometimes they don't."
It was Isner's first match on clay since last September and it showed.
"That's not an easy turnaround so I tried to keep my composure," Isner said. "I haven't really played great this year, so I knew it was going to be a little bit of a mental battle."
Qualifier Robby Ginepri of the United States kept eighth-seeded Michael Russell of the United States off balance most of the match for a 6-2, 6-2 victory.
Top-seeded Nicolas Almagro of Spain plays his first match Wednesday night against Gael Monfils of France. Monfils, who missed most of last season with a knee strain, beat James Blake of the United States in the first round.
Verdasco won the tiebreaker when Johnson double-faulted at set point. Johnson held after four break points in the fourth game of the second set, but he was broken in the sixth and eighth games.
Ginepri broke Russell quickly in the first game of the match and again in the seventh game and wrapped up the first set in the eighth game. He was aided by three Russell errors and he served an ace on the first set point.
Ginepri took control of the match in the opening game of the second set, breaking Russell at the fifth break point. Ginepri pounded in several down-the-line winners that left Russell flat-footed.
"Against the faster players, you wrong foot them and hit behind them, gives them less of a chance to react," Ginepri said. "That was my game plan today and my backhand was working well at the line. A lot of my shots were pushing him back and I never let him get set up today, which was the big difference."