The 28-year-old Sydneysider was aided by facing an opponent struggling with injury on a windy Wednesday in Switzerland before Spain's seventh seed Bernabe Zapata Miralles finally retired from their second-round tie when trailing 0-6 0-3.
But in the week before Roland Garros, it gave O'Connell, who reached his first clay-court semi-final in Munich last month while beating Olympic champ Alexander Zverev en route, a last-eight date with Grigor Dimitrov on Thursday.
Bulgarian wildcard Dimitrov, who won his only previous meeting with O'Connell in straight sets at the Australian Open six years ago, looked impressive while dismissing Roberto Carballes Baena 6-1 6-4 to reach his first tour-level quarter-final on clay this year.
"Honestly, it was a good day," Dimitrov said.
"It was windy, kind of swirly, a little bit cold … I felt all I had to do was be very composed, look after the points and simply follow (my) game plan."
World No.85 O'Connell, though, will go into the clash, boosted by the knowledge that he'll travel to Paris on a career-high ranking of at least No.76, topping his summit of No.78 last November.
Victory over Dimitrov would put the man who's currently ranked seventh in Australia up in the mix in Paris to challenge Max Purcell for his national No.3 spot behind Alex de Minaur and the currently injured Nick Kyrgios.
Favourite in Geneva will be top seeded Norwegian Casper Ruud, who began his title defence by beating American J.J. Wolf 6-3 7-5.
The world No.4 can seemingly do no wrong on these courts, where his record now stands at 9-0 after winning back-to-back titles. Last year, it proved the prelude to him making the final against Rafael Nadal in Paris.
Ruud will next face Nicolas Jarry in the quarters, while second seed Taylor Fritz will play Ilya Ivashka after he won his all-American clash with Marcos Giron 4-6 6-2 6-3.
In the other pre-Roland Garros tournament at the Lyon Open in France, defending champ Cameron Norrie moved into the last eight with a 6-3 6-4 victory over David Goffin.
The Briton needed just under 90 minutes to defeat the Belgian, saving five break points before setting up a meeting with Sebastian Baez.
Top seed Felix Auger-Aliassime beat qualifier Pablo Llamas Ruiz 7-5 6-2 while American Tommy Paul edged out Frenchman Gregoire Barrere 7-6 (8-6) 4-6 6-3.
