The Serb and reigning Wimbledon champ continued his near perfect summer of tennis and is now 54-1 in singles matches this season.
"I was happy with the way I played so overall it has been a good performance," said Djokovic who won in Montreal last week for his ninth career singles title.
"I am a more confident player now and I have more belief that I can win the big matches. I feel much more complete than I was last couple of years."
In other matches involving top seeded men on Wednesday, Britain's Andy Murray defeated Argentina's David Nalbandian, 6-4, 6-1 and second seed Rafael Nadal beat qualifier Julien Benneteau 6-4, 7-5 despite having to play with two fingers on his right hand in bandages after burning them on a hot plate.
On the women's side, top ranked Caroline Wozniacki was upset for the second straight week, losing to unheralded American Christine McHale 6-4, 7-5 and American veteran Serena Williams withdrew from the tournament ahead of her second-round match due to a foot problem.
Djokovic needed just 76 minutes to dispatch Harrison, hitting three aces and winning 73 percent of his first serves.
He said part of the reason for his success this season is he never takes opponents for granted whether they are a top 10 player or a qualifier.
"There is always motivation for me," Djokovic said. "Every time I step on court I want to win. That keeps me going. I have a couple of tournaments I want to do well in over next few months and US Open is one."
The 19-year-old Harrison lost his cool several times during the match and was given a warning by the chair umpire in the second set for smashing balls into the crowd.
He had six aces but served poorly, winning just 50 percent of his first serve points.
Murray beat Nalbandian for the third consecutive time after losing the first two career matches against the Argentinian.
Murray easily advanced to the third round where he will face American Alex Bogomolov who beat Jo-Winfried Tsonga 6-3, 6-4.
"I was definitely better today," Murray said. "I need to try and keep that up for the next match and hopefully play just five percent, 10 percent better tomorrow than I did today. I'll be happy with that."
Murray broke Nalbandian's serve six times and fired five aces, spending just 77 minutes on the court.
"I took quite a long break after Wimbledon and obviously played pretty poorly last week, so wanted to up my game and hopefully get a few matches this week and try and go all the way here if I can," Murray said. "And hopefully I play my best tennis at the US Open. That's the end goal."
World number one Wozniacki's disappointing US Open preparations continued Wednesday as she crashed out. The 21-year-old Dane's loss resembled her collapse last week in Toronto, where she went out in the second round after letting a 5-1 lead slip away in the second set.
Wozniacki - a finalist at the 2009 US Open and the winner of five titles so far this year - was philosophical about her poor form and vowed to put it right.
"Such things happen during a season, to have highs and lows," Wozniacki said.
"I am going to come back stronger and win matches very soon," she added. "I cannot remember the last time that I lost my first match on successive occasions. But such things happen."
Williams was on a run of 12 straight wins after successive titles at Stanford and Toronto, but the 29-year-old said she aggravated an injury to the big toe on her right foot.
"I felt a pain while playing (in the first round on Tuesday) and I don't think it's the right time to be taking risks," said Williams, who underwent a foot operation after winning Wimbledon in July 2010.
Williams' withdrawal allowed Australian world number 10 Samantha Stosur - who lost to the American in the Toronto final on Sunday - to advance to a third-round contest with Chinese world number five Li Na.
Djokovic, Murray, Nadal cruise at Cincinnati
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