1985–2002: Established actor
He achieved a breakthrough with his role as the subdued protagonist Sam Lowry in the Terry Gilliam science fiction dystopian dark comedy, Brazil (1985). After Brazil, Pryce appeared in the historical thriller The Doctor and the Devils (also 1985) and then in the Gene Wilder-directed film Haunted Honeymoon (1986). During this period of his life, Pryce continued to perform on stage, and gained particular notice as the successful but self-doubting writer Trigorin in a London production of Anton Chekhov's The Seagull in late 1985. From 1986 to 1987 Pryce played the lead part in the Royal Shakespeare Company's production of Macbeth, which also starred Sinéad Cusack as Lady Macbeth. Pryce worked once again with Gilliam in The Adventures of Baron Munchausen (1988), playing "The Right Ordinary Horatio Jackson". The film was a notorious financial fiasco, with production costing more than $40 million, when the original budget was $23.5 million. The following year Pryce appeared in three of the earliest episodes of the improvisation show Whose Line Is It Anyway?, alongside Paul Merton and John Sessions, and in Uncle Vanya, again a play by Chekhov, at the Vaudeville Theatre. After a series of major dramatic roles on stage, including Vanya and Macbeth, Pryce decided he wanted to do musicals after seeing his friend Patti LuPone in the original London production of Les Misérables.
He successfully returned to the stage in 1990 originating the role of The Engineer, a Eurasian pimp, in the West End musical Miss Saigon. His performance was praised in England where he won the Olivier and Variety Club awards, but when the production transferred to Broadway the Actors' Equity Association (AEA) tried to stop Pryce from portraying The Engineer because, according to their executive secretary, "[t]he casting of a Caucasian actor made up to appear Asian is an affront to the Asian community." The London production featured Pryce in yellowface, wearing prosthetics to alter the shape of his eyes and makeup to alter the colour of his skin. The show's producer, Cameron Mackintosh, decided to cancel the $10 million New York production. Realising that its decision would result in the loss of many jobs, and after Pryce received much support from fellow actors (both Charlton Heston and John Malkovich threatened to leave the union if Pryce was not allowed to perform) the AEA decided to make a deal with Mackintosh, allowing Pryce to appear in the production. He won a Tony Award for his performance in 1991. The controversy over Pryce's casting in Miss Saigon provided playwright David Henry Hwang the inspiration for his plays Face Value and Yellow Face.
Made in the same period, Pryce starred in the ITV mini-series Selling Hitler (1991) as Gerd Heidemann. Pryce returned to the London stage the following year to star for one night only at the Royal Festival Hall for an AIDS charity alongside Elaine Paige and Lilliane Montivecchi in the 1992 revival of the Federico Fellini-inspired musical Nine. He appeared in the film Glengarry Glen Ross (1992), an adaptation of the David Mamet play. Pryce featured, alongside Kathy Burke and Minnie Driver, in the BBC serial Mr. Wroe's Virgins (1993), directed by Danny Boyle. Pryce played Henry Kravis in the HBO produced made-for-TV movie Barbarians at the Gate (1993). He was nominated for a Primetime Emmy Award and for a Golden Globe Award for his role. Also during 1993, Pryce appeared in Martin Scorsese's The Age of Innocence, and starred alongside River Phoenix and Judy Davis in the unfinished film Dark Blood, but production had to be shut down when, 11 days short of completion, Phoenix died from a drug overdose. Director George Sluizer, who owns the rights to what has been filmed, has made available some of the raw material, which features Pryce and Phoenix on a field in Utah, on his personal website. Between 1993 and 1997, Pryce, on a multimillion-dollar contract became the spokesman for the Infiniti automobile marque in a series of American television commercials, in particular for the Infiniti J30 and Infiniti Q45. In one of these advertisements Pryce appeared alongside jazz singer Nancy Wilson in a Prague nightclub. In 1994, Pryce portrayed Fagin in a revival of the musical Oliver!, and starred alongside Emma Thompson in the film Carrington (1995), which centres on a platonic relationship between gay writer Lytton Strachey and painter Dora Carrington. For his portrayal of Strachey, Pryce received the Best Actor Award at the 1995 Cannes Film Festival. His film roles during this time included Evita (1996) and Tomorrow Never Dies (1997).
During the early 2000s Pryce starred and participated in a variety of movies, such as The Affair of the Necklace (2001), and Unconditional Love (2002). While the success of some of these films was variable, the 2001 London stage production of My Fair Lady and his portrayal of Professor Henry Higgins was acclaimed by observers. Martine McCutcheon, who portrayed Eliza Doolittle, was sick during much of the show's run. McCutcheon was replaced by her understudy Alexandra Jay, who would also fall sick hours before a performance, forcing her understudy, Kerry Ellis, to take the lead. On her first night, Pryce introduced Ellis to the audience before the show by saying "This will be your first Eliza, my second today and my third this week. Any member of the audience interested in playing Eliza can find applications at the door. Wednesday and Saturday matinee available." Pryce performed with four Elizas during the course of 14 months. The show was nominated for four Laurence Olivier Awards on 2001: Best Actress in a Musical for Martine McCutcheon, Outstanding Musical Production, Best Theatre Choreographer and Best Actor in a Musical for Pryce. Pryce lost to Philip Quast, and McCutcheon won in her category.