diff --git a/distributed/client.py b/distributed/client.py
index 422b3efbf9..882b4cb905 100644
--- a/distributed/client.py
+++ b/distributed/client.py
@@ -33,14 +33,14 @@
 import dask
 from dask.base import (
     collections_to_dsk,
+    newstyle_collections,
     normalize_token,
     tokenize,
-    newstyle_collections,
 )
 from dask.core import flatten, validate_key
 from dask.highlevelgraph import HighLevelGraph, TaskFactoryHLGWrapper
 from dask.optimization import SubgraphCallable
-from dask.typing import no_default, DaskCollection2
+from dask.typing import DaskCollection2, no_default
 from dask.utils import (
     apply,
     ensure_dict,
@@ -1966,6 +1966,7 @@ def submit(
 
         futures = self._graph_to_futures(
             dsk,
+            [key],
             workers=workers,
             allow_other_workers=allow_other_workers,
             internal_priority={key: 0},
@@ -2171,6 +2172,7 @@ def map(
 
         futures = self._graph_to_futures(
             dsk,
+            keys,
             workers=workers,
             allow_other_workers=allow_other_workers,
             internal_priority=internal_priority,
@@ -3109,6 +3111,7 @@ def _get_computation_code(
     def _graph_to_futures(
         self,
         dsk,
+        keys,
         workers=None,
         allow_other_workers=None,
         internal_priority=None,
@@ -3141,9 +3144,6 @@ def _graph_to_futures(
             # Merge global and local annotations
             annotations = merge(dask.get_annotations(), annotations)
 
-            # Pack the high level graph before sending it to the scheduler
-            keys = dsk.__dask_output_keys__()
-
             # Validate keys
             for key in keys:
                 validate_key(key)
@@ -3259,6 +3259,7 @@ def get(
         dsk = TaskFactoryHLGWrapper.from_low_level(dsk, list(flatten(keys)))
         futures = self._graph_to_futures(
             dsk,
+            keys,
             workers=workers,
             allow_other_workers=allow_other_workers,
             resources=resources,
@@ -3449,6 +3450,7 @@ def compute(
         if newstyle_collections(variables):
             variables = [var.finalize_compute() for var in variables]
             dsk = collections_to_dsk(variables, optimize_graph, **kwargs)
+            names = dsk.__dask_output_keys__()
         else:
             dsk = collections_to_dsk(variables, optimize_graph, **kwargs)
             names = ["finalize-%s" % tokenize(v) for v in variables]
@@ -3468,10 +3470,13 @@ def compute(
             layers.update(dsk.layers)
             dependencies = {finalize_name: set(dsk.layers.keys())}
             dependencies.update(dsk.dependencies)
-            dsk = TaskFactoryHLGWrapper(HighLevelGraph(layers, dependencies), out_keys=names)
+            dsk = TaskFactoryHLGWrapper(
+                HighLevelGraph(layers, dependencies), out_keys=names
+            )
 
         futures_dict = self._graph_to_futures(
             dsk,
+            keys=names,
             workers=workers,
             allow_other_workers=allow_other_workers,
             resources=resources,
@@ -3481,7 +3486,7 @@ def compute(
             actors=actors,
         )
 
-        futures = list(futures_dict.values())
+        futures = [futures_dict[name] for name in names]
 
         if sync:
             result = self.gather(futures)
@@ -3570,6 +3575,7 @@ def persist(
 
         futures = self._graph_to_futures(
             dsk,
+            dsk.__dask_output_keys__(),
             workers=workers,
             allow_other_workers=allow_other_workers,
             resources=resources,
diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index 5ec40959fd..8983db44ba 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -55,7 +55,6 @@
 from dask.core import get_deps, validate_key
 from dask.typing import Key, no_default
 from dask.utils import (
-    ensure_dict,
     format_bytes,
     format_time,
     key_split,
@@ -140,7 +139,6 @@
     from typing_extensions import TypeAlias
 
     from dask.typing import TaskGraphFactory
-    from dask.highlevelgraph import HighLevelGraph
 
 # Not to be confused with distributed.worker_state_machine.TaskStateState
 TaskStateState: TypeAlias = Literal[
@@ -4670,6 +4668,15 @@ async def update_graph(
         try:
             try:
                 graph_factory = deserialize(graph_header, graph_frames).data
+                if list(graph_factory.__dask_output_keys__()) != list(keys):
+                    # Note: If we no longer want to rely on tokenization to be
+                    # consistent beyond an interpreter session, we could
+                    # implement this in a way that the scheduler sends a signal
+                    # back to the client with the final key names
+                    # This would be easiest with a version of https://github.com/dask/distributed/issues/7480
+                    raise RuntimeError(
+                        "Catastrophic failure. Tokenization of keys unstable!"
+                    )
                 del graph_header, graph_frames
             except Exception as e:
                 msg = """\