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The former world number three beat Taro Daniel 7-5 6-4 on Thursday (AEDT), winning 82 per cent of his first-serve points in an encouraging performance as he attempts to win a ninth indoor Tour title.
Should Cilic lift the trophy, he would join Roger Federer (103), Rafael Nadal (86), Novak Djokovic (82), Andy Murray (46) and Juan Martin del Potro (22) as the only active male players to win at least 20 Tour-level titles.
"It is the beginning of the season and my third match of the year, so I am still feeling a little bit rusty," said Cilic. "Overall, it was a solid match. [It is] something I definitely needed for the start of the tournament."
The Croatian will face Kwon Soon-woo in the quarter-finals, while Yoshihito Nishioka and Alexander Bublik were among the others to progress.
Jannik Sinner was a surprise casualty at the Open Sud de France, the world number 34 losing in three sets to Aljaz Bedene in a match that lasted nearly two hours and 40 minutes.
Sixth seed Ugo Humbert battled past Dutch qualifier Tallon Griekspoor in a match with three tie-breaks, while second seed David Goffin went the distance to overcome wildcard Benjamin Bonzi 4-6 6-4 7-5.