Quins lost their opening two matches of Pool Four but successive wins against Racing have revived hopes of reaching the quarter-finals.
Clermont, who top the group by four points, must now travel to London on the second weekend of January in the pivotal fixture.
Racing paraded four Lions in Jamie Roberts, Jonathan Sexton, Mike Phillips and Dan Lydiate and O’Shea questioned the wisdom of paying large salaries.
“Over two weekends we’ve taken nine points out of a possible 10 against a Racing team with a large squad,” the club’s director of rugby said. “We were the better team, with emphasis on team, and that’s what made the big difference. Racing had four Lions who started the third Test against Australia out there. Money can help, but it takes time.”
Once Quins have faced Heineken Cup heavyweights Clermont, they travel to Scarlets as they seek to complete a remarkable comeback by progressing to the knockout stages.
“Northampton showed against Leinster at the Aviva Stadium what character, physicality and sheer will can do,” O’Shea said. “We have that in abundance as well. Securing a losing bonus point at Clermont in October was bit of a turning point in terms of rediscovering ourselves. We know exactly what we have to do.”
HARLEQUINS: Brown, Walker, Hopper, Molenaar, Smith, Evans, Care; Marler, Ward, Collier, Matthews, Robson, Wallace, Robshaw, Easter.
Replacements: Botica for Evans (41), Dickson for Care (78), Lambert for Marler (73), Doran-Jones for Collier (29), Kennedy for Matthews (55), Trayfoot for Robson (78).
RACING METRO 92: Hernandez, Plante, Chavancy, Roberts, Vakatawa, Sexton, Phillips; Khinchagishili, Lacombe, Tonga’uiha, Metz, Ghezal, Lydiate, Battut, Gerondeau.
Replacements: Fall for Vakatawa (75), Wisniewski for Sexton (64), Machenaud for Phillips (63), Ben Arous for Khinchagishili (53), Kruger for Ghezal (63), Ducalcon for Lydiate (16).
Referee: Alain Rolland (Ireland).