Needing to win to keep their hopes alive, Hanazono conceded the opening try to former Western Force and Brumbies centre Chance Peni, but held the Division Two champions scoreless for the remaining 68 minutes, with Cooper's long-time halves partner Will Genia one of the game's stars.
The veteran Wallaby scrum-half scored his 10th try of the season, one behind ex-England flyhalf Freddie Burns.
The former Queensland Reds Super Rugby winners will face their ex-Test teammate Tom Banks in the home-and-away series after the Wallaby fullback's Mie Heat ended the regular season with a hefty 67-22 loss to seventh-placed Black Rams Tokyo on Sunday.
Israel Folau and Samu Kerevi enjoyed a better return in the final match before their two-game relegation series against the Shuttles, as Urayasu D-Rocks won their third match of the season, beating Sagamihara Dynaboars 34-21.
Kobe Steelers are going to have to reverse back-to-back defeats against Shizuoka BlueRevs if they are to make it beyond the first weekend of the Division One playoffs.
Former Wallaby coach Dave Rennie's charges head into their third fixture of the season against the BlueRevs coming off a 29-23 defeat on Saturday, which added to a 15-13 loss at Shizuoka on the competition's opening day.
Kobe led 20-19 shortly after halftime, but were outscored four tries to two.
The winner of Saturday's opening quarter-final will play the defending champions Brave Lupus Tokyo, who will skip the first week after overpowering Yokohama Eagles 49-28 to finish on top of the table
The Robbie Deans-coached Saitama Wild Knights also gained direct entry to the final four after recording their biggest win of the season, flattening Tokyo Sungoliath 60-17.
They will play the winners of Sunday's match between Bernard Foley's Spears Funabashi Tokyo-Bay and Sungoliath.
Spears ended the regular season third after Saturday's 37-14 win over Verblitz.
