Isner, the tournament's top seed and two-time champion, served 17 aces and needed just 68 minutes to oust the 13th-seeded Kukushkin in the final tuneup for next week's US Open.
"It could've gone a lot quicker," said Isner, who was born in nearby Greensboro, N.C. "I made it tough on myself, which I'm not too pleased about because of how I was serving. Still, I played well at the end of the match and I'm off in straight sets again, which is nice."
The 6-foot-10 Isner broke Kukushkin's serve twice and won nearly three-quarters of all points played in the first set, which he completed in just 18 minutes.
However, Isner had a tougher time in the second set. While he served 12 aces, he also struggled to finish points against the smaller Kukushkin.
"I was putting a lot of pressure on him and doing the right things," Isner said. "But I got away from that a little bit. Of course, he changed his tactics up and certainly played better in the second set. It got away from me there a little bit, but I played well at the end."
Isner, 12-0 all-time in the tournament, will face seventh-seeded Lukas Rosol of the Czech Republic in Thursday's quarterfinals. Rosol advanced with a 1-6, 6-2, 6-2 victory over 10th-seeded Pablo Andujar of Spain.
Also advancing to the quarterfinals were American Sam Querrey, fifth-seeded Guillermo Garcia-Lopez of Spain, Belgian qualifier David Goffin, Poland's Jerzy Janowicz, ninth-seeded Yen-Hsun Lu of Taiwan and 14th-seeded Andreas Seppi of Italy.
Querrey will play Garcia-Lopez in one quarterfinal match at the Wake Forest Tennis Center. The other pairings have Goffin facing Janowicz and Lu taking on Seppi.
In earlier matches, Garcia-Lopez battled through a third-set tiebreaker before beating 11th-seeded Donald Young of the U.S. 6-7 (4-7), 6-3, 7-6 (8-6).
Garcia-Lopez overcame a 6-4 deficit in the third tiebreaker by winning four consecutive points to advance to an ATP tournament quarterfinal for the sixth time this year.
"The last month in Europe on the clay courts, I was losing a lot of tiebreakers," said Garcia-Lopez, who won his third career ATP Tour title in April in Morocco.
"But at the end today, I got lucky. Sometimes the tiebreaker is a lottery, and I got the number. That's why I won."
In other third-round matches, Querrey defeated second-seeded Kevin Anderson of South Africa 7-6 (7-4), 6-4; Goffin extended his winning streak to 25 consecutive matches by beating 15th-seeded Jarkko Nieminen of Finland 6-4, 4-6, 6-4; Janowicz downed 12th-seeded Edouard Roger-Vasselin of France 4-6, 6-3, 6-4; Lu beat No. 8 seed Marcel Granollers of Spain 6-1, 6-2; and Seppi defeated France's Nicolas Mahut 6-4, 7-6 (9-7).