diff --git a/src/tools/miri/README.md b/src/tools/miri/README.md
index 640a953dac9..79b0daf9e82 100644
--- a/src/tools/miri/README.md
+++ b/src/tools/miri/README.md
@@ -389,7 +389,7 @@ to Miri failing to detect cases of undefined behavior in a program.
   Follow [the discussion on supporting other types](https://github.com/rust-lang/miri/issues/2365).
 * `-Zmiri-measureme=<name>` enables `measureme` profiling for the interpreted program.
    This can be used to find which parts of your program are executing slowly under Miri.
-   The profile is written out to a file with the prefix `<name>`, and can be processed
+   The profile is written out to a file inside a directory called `<name>`, and can be processed
    using the tools in the repository https://github.com/rust-lang/measureme.
 * `-Zmiri-mute-stdout-stderr` silently ignores all writes to stdout and stderr,
   but reports to the program that it did actually write. This is useful when you
diff --git a/src/tools/miri/src/machine.rs b/src/tools/miri/src/machine.rs
index 21c5a9c1b70..32717a0d28b 100644
--- a/src/tools/miri/src/machine.rs
+++ b/src/tools/miri/src/machine.rs
@@ -4,6 +4,8 @@
 use std::borrow::Cow;
 use std::cell::RefCell;
 use std::fmt;
+use std::path::Path;
+use std::process;
 
 use rand::rngs::StdRng;
 use rand::SeedableRng;
@@ -498,7 +500,21 @@ impl<'mir, 'tcx> MiriMachine<'mir, 'tcx> {
         let layouts =
             PrimitiveLayouts::new(layout_cx).expect("Couldn't get layouts of primitive types");
         let profiler = config.measureme_out.as_ref().map(|out| {
-            measureme::Profiler::new(out).expect("Couldn't create `measureme` profiler")
+            let crate_name = layout_cx
+                .tcx
+                .sess
+                .opts
+                .crate_name
+                .clone()
+                .unwrap_or_else(|| "unknown-crate".to_string());
+            let pid = process::id();
+            // We adopt the same naming scheme for the profiler output that rustc uses. In rustc,
+            // the PID is padded so that the nondeterministic value of the PID does not spread
+            // nondeterminisim to the allocator. In Miri we are not aiming for such performance
+            // control, we just pad for consistency with rustc.
+            let filename = format!("{crate_name}-{pid:07}");
+            let path = Path::new(out).join(filename);
+            measureme::Profiler::new(path).expect("Couldn't create `measureme` profiler")
         });
         let rng = StdRng::seed_from_u64(config.seed.unwrap_or(0));
         let borrow_tracker = config.borrow_tracker.map(|bt| bt.instantiate_global_state(config));