diff --git a/sdk/storage/azblob/blockblob/chunkwriting.go b/sdk/storage/azblob/blockblob/chunkwriting.go
index 0ed98c403281..0bcd4b3686f3 100644
--- a/sdk/storage/azblob/blockblob/chunkwriting.go
+++ b/sdk/storage/azblob/blockblob/chunkwriting.go
@@ -13,12 +13,12 @@ import (
 	"encoding/binary"
 	"errors"
 	"fmt"
-	"github.com/Azure/azure-sdk-for-go/sdk/storage/azblob/internal/shared"
 	"io"
 	"sync"
 	"sync/atomic"
 
 	"github.com/Azure/azure-sdk-for-go/sdk/internal/uuid"
+	"github.com/Azure/azure-sdk-for-go/sdk/storage/azblob/internal/shared"
 )
 
 // blockWriter provides methods to upload blocks that represent a file to a server and commit them.
@@ -188,9 +188,7 @@ func (c *copier) write(chunk copierChunk) {
 
 // close commits our blocks to blob storage and closes our writer.
 func (c *copier) close() error {
-	c.wg.Wait()
-
-	if err := c.getErr(); err != nil {
+	if err := c.waitForFinish(); err != nil {
 		return err
 	}
 
@@ -200,6 +198,44 @@ func (c *copier) close() error {
 	return err
 }
 
+// waitForFinish waits for all writes to complete while combining errors from errCh
+func (c *copier) waitForFinish() error {
+	var err error
+	done := make(chan struct{})
+	go func() {
+		// when write latencies are long, several errors might have occurred
+		// drain them all as we wait for writes to complete.
+		err = c.drainErrs(done)
+	}()
+
+	c.wg.Wait()
+	close(done)
+	return err
+}
+
+// drainErrs drains all outstanding errors from writes
+func (c *copier) drainErrs(done chan struct{}) error {
+	var err error
+	for {
+		select {
+		case <-done:
+			return err
+		default:
+			if writeErr := c.getErr(); writeErr != nil {
+				err = combineErrs(err, writeErr)
+			}
+		}
+	}
+}
+
+// combineErrs combines err with newErr so multiple errors can be represented
+func combineErrs(err, newErr error) error {
+	if err == nil {
+		return newErr
+	}
+	return fmt.Errorf("%s, %w", err.Error(), newErr)
+}
+
 // id allows the creation of unique IDs based on UUID4 + an int32. This auto-increments.
 type id struct {
 	u   [64]byte
diff --git a/sdk/storage/azblob/blockblob/chunkwriting_test.go b/sdk/storage/azblob/blockblob/chunkwriting_test.go
index afbf7c0e63da..addc3fbd97be 100644
--- a/sdk/storage/azblob/blockblob/chunkwriting_test.go
+++ b/sdk/storage/azblob/blockblob/chunkwriting_test.go
@@ -30,6 +30,7 @@ type fakeBlockWriter struct {
 	path       string
 	block      int32
 	errOnBlock int32
+	stageDelay time.Duration
 }
 
 func newFakeBlockWriter() *fakeBlockWriter {
@@ -49,7 +50,12 @@ func newFakeBlockWriter() *fakeBlockWriter {
 
 func (f *fakeBlockWriter) StageBlock(_ context.Context, blockID string, body io.ReadSeekCloser, _ *StageBlockOptions) (StageBlockResponse, error) {
 	n := atomic.AddInt32(&f.block, 1)
-	if n == f.errOnBlock {
+
+	if f.stageDelay > 0 {
+		time.Sleep(f.stageDelay)
+	}
+
+	if f.errOnBlock > -1 && n >= f.errOnBlock {
 		return StageBlockResponse{}, io.ErrNoProgress
 	}
 
@@ -192,6 +198,45 @@ func TestGetErr(t *testing.T) {
 	}
 }
 
+func TestSlowDestCopyFrom(t *testing.T) {
+	p, err := createSrcFile(_1MiB + 500*1024) //This should cause 2 reads
+	if err != nil {
+		panic(err)
+	}
+	defer func(name string) {
+		_ = os.Remove(name)
+	}(p)
+
+	from, err := os.Open(p)
+	if err != nil {
+		panic(err)
+	}
+	defer from.Close()
+
+	br := newFakeBlockWriter()
+	defer br.cleanup()
+
+	br.stageDelay = 200 * time.Millisecond
+	br.errOnBlock = 0
+
+	errs := make(chan error, 1)
+	go func() {
+		_, err := copyFromReader(context.Background(), from, br, UploadStreamOptions{})
+		errs <- err
+	}()
+
+	ctx, cancel := context.WithTimeout(context.Background(), time.Second)
+	defer cancel()
+
+	select {
+	case <-ctx.Done():
+		failMsg := "TestSlowDestCopyFrom(slow writes shouldn't cause deadlock) failed: Context expired, copy deadlocked"
+		t.Error(failMsg)
+	case <-errs:
+		return
+	}
+}
+
 func TestCopyFromReader(t *testing.T) {
 	t.Parallel()