Carter, who won the French title with Racing last year, kicked seven points in the 22-13 victory on Sunday (NZ Time) to propel his Paris club into the semifinals.
Former All Blacks wing Joe Rokocoko scored one of Racing's three tries as the defending champions ended former Springboks World Cup winning coach Jake White's tenure at Montpellier.
Racing fielded four ex-All Blacks - Carter, Rokocoko, Casey Laulala and Chris Masoe - with a fifth Kiwi, Ben Tameifuna in the front row.
Racing survived an early injury to wing Juan Imhoff with his replacement, Teddy Thomas, and Leone Nakarawa scoring first half tries for a 14-10 halftime lead.
Francois Steyn - one of six South Africans in Montpellier's starting lineup - was yellow carded early in the second half but the home side cut the deficit to one point through Demetri Catrakilis' second penalty of the game.
Rokocoko struck the decisive blow with a 75th minute, with Carter missing the conversion.
But Racing held on for a deserved win with Montpellier reduced to 14 men for the final few minutes after Springbok prop Jannie du Plessis was sent off for punching a Racing rival.
Racing will play second-ranked Clermont Auvergne in next Sunday's semifinals while Ma'a Nonu's Toulon will face former All Blacks and Hurricanes Team-mates Victor Vito and Jason Eaton's La Rochelle on Saturday.
Toulon beat Castres 26-22 in the playoffs last Saturday after a try, two conversions and four penalties to Wales and British and Irish Lions fullback Leigh Halfpenny.
Castres, who fielded former Blues wing David Smith, could only manage a penalty try and five penalties to Benjamin Urdapilleta.
Photo: REUTERS Dan Carter has helped the Crusaders make the French top 14 semifinals.