Boyle, who went on to score eight Oscars with his last film Slumdog Millionaire, collaborated with Rahman again for 127 Hours, a biopic on the life of mountain climber Aron Ralston.
Rahman, however, lost the best score trophy to Trent Reznor and Atticus Ross for their film The Social Network. The movie on the life of Facebook founder also bagged top honours including best film, best director and best adapted screenplay.
The awards, presented by the Broadcast Film Critics Association, are considered a strong indicator for the Oscar awards. Most of the Critics' Choice Awards winners do well at the Oscars.
British actor Colin Firth was named the best actor for his role as a stuttering king in The King's Speech while Natalie Portman's turn as a disturbed ballerina in Black Swan won her the best actress trophy.
Christian Bale was named the best supporting actor for his role in real-life drama The Fighter, which also saw Melissa Leo winning the best supporting actress nod.
Leonardo DiCaprio starrer Inception led all films with six awards total but most of them were for technical achievement.
