Uruguayan veteran Suarez scored just 32 seconds into the game and added a second five minutes later as Miami, without injured superstar Lionel Messi, secured their place in the post-season.
Miami are eight points clear of second-placed Cincinnati in the Eastern Conference.
Messi has not played since he suffered an ankle injury in Argentina's win over Colombia in the final of Copa America on July 14.
But Miami expect Messi will be back before the end of the regular season which concludes on October 19 with the play-offs beginning the following week.
Cincinnati humiliated Miami with a 6-1 victory over Gerardo Martino's team in Ohio on July 6th and the way the game started indicated Inter were determined to avenge that loss.
Yannick Bright fed Marcelo Weigandt down the right and the Argentine found Suarez who brought the ball down before burying it in the net.
With former NFL great Tom Brady watching on in the company of Miami co-owner David Beckham, former Barcelona striker Suarez then doubled the advantage with another clinical finish after a smart one-two with Matias Rojas.
Miami looked in firm control of the game until three minutes before the break, when their Argentine defender Tomas Aviles was sent off for a second yellow card after a reckless, lunging challenge on Kevin Kelsy.
At the break, Cincinnati brought on Luciano Acosta, the league's reigning Most Valuable Player - who is returning from an injury absence.
And while the Argentine added a creative edge in the second half, he wasn't able to stop Cincinnati from suffering a fourth straight loss in the league.
Miami kept their shape and discipline as they protected their lead with Italian midfielder Bright delivering another impressive performance.
