However, fellow Aviva Premiership side Northampton were unable to join them in the last eight of the cup competition after suffering two defeats.
Gloucester, winners of the JP Morgan Sevens last weekend, sealed their quarter-final berth after bouncing back from an opening loss to VVA Moscow Saracens Region (19-12) with victories over New York City (26-24) and Western Province (27-17).
That left the Cherry and Whites at the top of Group A with 11 points, with Moscow also progressing in second spot with 10 points, while New York's nine-point haul saw them through as one of the two best third-placed teams.
Dan Robson, who scored twice in the win over New York as Gloucester fought back from 24-12 down, said on www.worldclub7srugby.com: "It took us a while to get into it and obviously we were disappointed to lose the first game.
"But the second two games we were awesome and we've still got a lot more to give. The second game filled the boys with confidence and we're really looking forward to tomorrow now."
Gloucester will next face Harlequins, who also went through as one of the best third-placed teams after finishing level on 10 points with the top two sides in Group B, Auckland and ACT Brumbies.
Like Gloucester, Quins lost their opener, going down 24-14 to the Brumbies, before recovering with victories Kuban Krasnodar (24-12) and Auckland (31-14).
It was not such a successful day for Northampton though as they could only finish third in Group C on five points behind Buenos Aires (12) and San Francisco (nine).
The Saints lost their opening two matches to Buenos Aires (30-0) and San Francisco (17-12) before finishing with a 17-7 victory over the winless Blue Bulls.
Northampton will now take part in the Plate and Shield competitions tomorrow, along with the Blue Bulls, Kuban Krasnador and Western Province.