Thank you for clearing that up for me! 
I realize now that my post didn’t exactly match the OP’s requirements. This one does: In a '60s war flick called The Secret Invasion, William Campbell impersonated the German commandant of the fortress where he and his fellow commandos were being held prisoner.
I like the moment where Orlando Bloom imitates Capt. Jack Sparrow in the first Pirates of the Caribbean movie.
There’s a 4th season episode of Buffy the Vampire Slayer where
Buffy and Faith swap bodies, and Gellar and Dushku do a great job of imitating each other
Well, there was “Turnabout Intruder” in Star Trek. Sandra Smith, as Janet Lester, does a great job of using Kirk’s mannerism.
Spike also does a spot-on impression of Angel, early on. “Say no more. Evil’s still afoot. And I’m almost out of that nancy-boy hair-gel I like so much. Quickly, to the Angel-mobile, away!”
House, who is British, but is speaking with an American accent, imitates the Australian Dr. Chase.
Eddie Murphy also imitates a young Damon Wayans and the Police Chief in Beverly Hills cop.
I think Eddie Murphy also imitates Charles Dance (Sardo Numspa) in “The Golden Child.”
I seem to remember Kevin Kline doing some Monty Pythonesque outbursts in “A Fish Called Wanda.”
In Stakeout, Richard Dreyfuss and Emilio Estevez play two detectives on a stakeout. To pass the time they play a game of trivia. Estevez’s character gives Dreyfuss’ character a movie quote. “Okay, ‘This was no boating accident,’” imitating Hooper, Dreyfuss’ character from “Jaws”. Dreyfuss says, “I don’t know.” Esteves responds, “Man, you suck at this.”
Enver Gjokaj does an uncanny imitation of Fran Kranz’s Topher character in an episode of Dollhouse.
Matt Damon birefly imitates his father, played by James Rebhorn, in The Talented Mr. Ripley.
Tom Cruise does a one-line imitation of Jack Nicholson in A Few Good Men.
Jack Nicholson’s Joker imitates Jack Palance in Batman. (“YOU . . . are my number one . . . GUY!”)
And as long as we’re including TV shows, Anna Torv does a surprisingly convincing impression of Leonard Nimoy in several episodes of Fringe. Her character is actually possessed by the character played by Nimoy, so this one falls under the same subcategory as Dollhouse and other body-switching scenarios.
Forgot to mention he imitates Phillip Seymour Hoffman in the same movie, imitating Hoffman’s character’s accent as well.
And vice versa: Shatner gives a good performance as the whacko Dr. Lester.
Jim Carrey does William Shatner in Pet Detective. He does Clint Eastwood in (I think) Pet Detective 2.
Yes, but Shatner was not in the first Pet Detective movie and Eastwood wasn’t in the second one. The actor being imitated needs to be in the same movie with the actor imitating him or her.
Since we’re on Star Trek, Jeri Ryan does a rather good if overdone Robert Picardo in the episode of Voyager where Picardo takes over her body. The trick is that Picardo actually did all the parts himself on video and she just mimicked them.
In RIO BRAVO, Walter Brennan does a wonderful John Wayne imitation.
One of the few good parts of The Matrix Revolutions is Ian Bliss’s spot-on Hugo Weaving impression when his character is possessed by Agent Smith.
There’s an outtake from “Star Trek’s” “Squire of Gothos” where Shatner mimics William Campbell’s somewhat effeminate demeanor.