diff --git a/src/compute/src/render/join/linear_join.rs b/src/compute/src/render/join/linear_join.rs
index c0ca286df04e..d7fb77324549 100644
--- a/src/compute/src/render/join/linear_join.rs
+++ b/src/compute/src/render/join/linear_join.rs
@@ -26,6 +26,7 @@ use mz_repr::{DatumVec, Diff, Row, RowArena};
 use mz_storage_client::types::errors::DataflowError;
 use mz_timely_util::operator::CollectionExt;
 
+use crate::render::context::ShutdownToken;
 use crate::render::context::{
     Arrangement, ArrangementFlavor, ArrangementImport, CollectionBundle, Context,
 };
@@ -123,6 +124,7 @@ where
                     inputs[stage_plan.lookup_relation].enter_region(inner),
                     stage_plan,
                     &mut errors,
+                    self.shutdown_token.clone(),
                 );
                 // Update joined results and capture any errors.
                 joined = JoinedFlavor::Collection(stream);
@@ -179,6 +181,7 @@ fn differential_join<G, T>(
         lookup_relation: _,
     }: LinearStagePlan,
     errors: &mut Vec<Collection<G, DataflowError, Diff>>,
+    shutdown_token: ShutdownToken,
 ) -> Collection<G, Row, Diff>
 where
     G: Scope,
@@ -223,13 +226,13 @@ where
         }
         JoinedFlavor::Local(local) => match arrangement {
             ArrangementFlavor::Local(oks, errs1) => {
-                let (oks, errs2) = differential_join_inner(local, oks, closure);
+                let (oks, errs2) = differential_join_inner(local, oks, closure, shutdown_token);
                 errors.push(errs1.as_collection(|k, _v| k.clone()));
                 errors.extend(errs2);
                 oks
             }
             ArrangementFlavor::Trace(_gid, oks, errs1) => {
-                let (oks, errs2) = differential_join_inner(local, oks, closure);
+                let (oks, errs2) = differential_join_inner(local, oks, closure, shutdown_token);
                 errors.push(errs1.as_collection(|k, _v| k.clone()));
                 errors.extend(errs2);
                 oks
@@ -237,13 +240,13 @@ where
         },
         JoinedFlavor::Trace(trace) => match arrangement {
             ArrangementFlavor::Local(oks, errs1) => {
-                let (oks, errs2) = differential_join_inner(trace, oks, closure);
+                let (oks, errs2) = differential_join_inner(trace, oks, closure, shutdown_token);
                 errors.push(errs1.as_collection(|k, _v| k.clone()));
                 errors.extend(errs2);
                 oks
             }
             ArrangementFlavor::Trace(_gid, oks, errs1) => {
-                let (oks, errs2) = differential_join_inner(trace, oks, closure);
+                let (oks, errs2) = differential_join_inner(trace, oks, closure, shutdown_token);
                 errors.push(errs1.as_collection(|k, _v| k.clone()));
                 errors.extend(errs2);
                 oks
@@ -262,6 +265,7 @@ fn differential_join_inner<G, T, J, Tr2>(
     prev_keyed: J,
     next_input: Arranged<G, Tr2>,
     closure: JoinClosure,
+    shutdown_token: ShutdownToken,
 ) -> (
     Collection<G, Row, Diff>,
     Option<Collection<G, DataflowError, Diff>>,
@@ -284,6 +288,10 @@ where
     if closure.could_error() {
         let (oks, err) = prev_keyed
             .join_core(&next_input, move |key, old, new| {
+                // Check the shutdown token to avoid doing unnecessary work when the dataflow is
+                // shutting down.
+                shutdown_token.probe()?;
+
                 let temp_storage = RowArena::new();
                 let mut datums_local = datums.borrow_with_many(&[key, old, new]);
                 closure
@@ -303,6 +311,10 @@ where
         (oks.as_collection(), Some(err.as_collection()))
     } else {
         let oks = prev_keyed.join_core(&next_input, move |key, old, new| {
+            // Check the shutdown token to avoid doing unnecessary work when the dataflow is
+            // shutting down.
+            shutdown_token.probe()?;
+
             let temp_storage = RowArena::new();
             let mut datums_local = datums.borrow_with_many(&[key, old, new]);
             closure