"Both of them are good players, especially on grass courts. I think they are dangerous guys," third seed Khachanov said.
Defending champion Borna Coric was in action against Joao Sousa of Portugal in the day's final match.
Unseeded Belgian David Goffin progressed to the quarters after he fought back to beat Moldova's Radu Albot 4-6 6-4 6-3.
Goffin sent down nine aces and will next face second seed Alexander Zverev or American Steve Johnson.
"It was not easy today. It was the first time I was playing on the centre court. It's different conditions compared to the outside court," Goffin said. "I'm happy with the way I fought."
Frenchman Pierre-Hugues Herbert was also made to work hard for victory, downing Ukrainian Sergiy Stakhovsky 2-6 7-6(2) 6-4.
Nine-times Halle champion Roger Federer is in second-round action on Thursday against France's Jo-Wilfried Tsonga.
(Reporting by Shubham Kalia in Bengaluru, editing by Ed Osmond)
