diff --git a/pkg/util/tracing/grpc_interceptor.go b/pkg/util/tracing/grpc_interceptor.go
index d5ad14fcab8d..87247f42bd04 100644
--- a/pkg/util/tracing/grpc_interceptor.go
+++ b/pkg/util/tracing/grpc_interceptor.go
@@ -356,12 +356,12 @@ func StreamClientInterceptor(tracer *Tracer, init func(*Span)) grpc.StreamClient
 			clientSpan.Finish()
 			return cs, err
 		}
-		return newTracingClientStream(cs, method, desc, clientSpan), nil
+		return newTracingClientStream(ctx, cs, desc, clientSpan), nil
 	}
 }
 
 func newTracingClientStream(
-	cs grpc.ClientStream, method string, desc *grpc.StreamDesc, clientSpan *Span,
+	ctx context.Context, cs grpc.ClientStream, desc *grpc.StreamDesc, clientSpan *Span,
 ) grpc.ClientStream {
 	finishChan := make(chan struct{})
 
@@ -386,8 +386,14 @@ func newTracingClientStream(
 		case <-finishChan:
 			// The client span is being finished by another code path; hence, no
 			// action is necessary.
-		case <-cs.Context().Done():
-			finishFunc(nil)
+		case <-ctx.Done():
+			// A streaming RPC can be finished by the caller cancelling the ctx. If
+			// the ctx is cancelled, the caller doesn't necessarily need to interact
+			// with the stream anymore (see [1]), so finishChan might never be
+			// signaled). Thus, we listen for ctx cancellation and finish the span.
+			//
+			// [1] https://pkg.go.dev/google.golang.org/grpc#ClientConn.NewStream
+			finishFunc(nil /* err */)
 		}
 	}()
 	otcs := &tracingClientStream{
diff --git a/pkg/util/tracing/grpc_interceptor_test.go b/pkg/util/tracing/grpc_interceptor_test.go
index fa3637a06457..c8f9ae0fb3cc 100644
--- a/pkg/util/tracing/grpc_interceptor_test.go
+++ b/pkg/util/tracing/grpc_interceptor_test.go
@@ -13,8 +13,8 @@ package tracing_test
 import (
 	"context"
 	"fmt"
+	"io"
 	"net"
-	"runtime"
 	"testing"
 
 	"github.com/cockroachdb/cockroach/pkg/testutils"
@@ -141,7 +141,10 @@ func TestGRPCInterceptors(t *testing.T) {
 
 	for _, tc := range []struct {
 		name string
-		do   func(context.Context) (*types.Any, error)
+		// expSpanName is the expected name of the RPC spans (client-side and
+		// server-side). If not specified, the test's name is used.
+		expSpanName string
+		do          func(context.Context) (*types.Any, error)
 	}{
 		{
 			name: "UnaryUnary",
@@ -156,11 +159,45 @@ func TestGRPCInterceptors(t *testing.T) {
 				if err != nil {
 					return nil, err
 				}
-				any, err := sc.Recv()
+				if err := sc.CloseSend(); err != nil {
+					return nil, err
+				}
+				var firstResponse *types.Any
+				// Consume the stream fully, as mandated by the gRPC API.
+				for {
+					any, err := sc.Recv()
+					if err == io.EOF {
+						break
+					}
+					if err != nil {
+						return nil, err
+					}
+					if firstResponse == nil {
+						firstResponse = any
+					}
+				}
+				return firstResponse, nil
+			},
+		},
+		{
+			// Test that cancelling the client's ctx finishes the client span. The
+			// client span is usually finished either when Recv() receives an error
+			// (e.g. when receiving an io.EOF after exhausting the stream). But the
+			// client is allowed to not read from the stream any more if it cancels
+			// the ctx.
+			name:        "UnaryStream_ContextCancel",
+			expSpanName: "UnaryStream",
+			do: func(ctx context.Context) (*types.Any, error) {
+				ctx, cancel := context.WithCancel(ctx)
+				defer cancel()
+				sc, err := c.UnaryStream(ctx, unusedAny)
 				if err != nil {
 					return nil, err
 				}
-				return any, sc.CloseSend()
+				if err := sc.CloseSend(); err != nil {
+					return nil, err
+				}
+				return sc.Recv()
 			},
 		},
 		{
@@ -186,7 +223,24 @@ func TestGRPCInterceptors(t *testing.T) {
 				if err := sc.Send(unusedAny); err != nil {
 					return nil, err
 				}
-				return sc.Recv()
+				if err := sc.CloseSend(); err != nil {
+					return nil, err
+				}
+				var firstResponse *types.Any
+				// Consume the stream fully, as mandated by the gRPC API.
+				for {
+					any, err := sc.Recv()
+					if err == io.EOF {
+						break
+					}
+					if err != nil {
+						return nil, err
+					}
+					if firstResponse == nil {
+						firstResponse = any
+					}
+				}
+				return firstResponse, nil
 			},
 		},
 	} {
@@ -214,20 +268,23 @@ func TestGRPCInterceptors(t *testing.T) {
 			}
 			require.Equal(t, 1, n)
 
+			expSpanName := tc.expSpanName
+			if expSpanName == "" {
+				expSpanName = tc.name
+			}
 			exp := fmt.Sprintf(`
 				span: root
 					span: /cockroach.testutils.grpcutils.GRPCTest/%[1]s
 						tags: span.kind=client
 					span: /cockroach.testutils.grpcutils.GRPCTest/%[1]s
 						tags: span.kind=server
-						event: structured=magic-value`, tc.name)
+						event: structured=magic-value`, expSpanName)
 			require.NoError(t, tracing.CheckRecordedSpans(finalRecs, exp))
 		})
 	}
-	// Force a GC so that the finalizer for the stream client span runs and closes
-	// the span. Nothing else closes that span in this test. See
-	// newTracingClientStream().
-	runtime.GC()
+	// Check that all the RPC spans (client-side and server-side) have been
+	// closed. SucceedsSoon because the closing of the span is async (although
+	// immediate) in the ctx cancellation subtest.
 	testutils.SucceedsSoon(t, func() error {
 		return tr.VisitSpans(func(sp tracing.RegistrySpan) error {
 			rec := sp.GetFullRecording(tracing.RecordingVerbose)[0]