diff --git a/src/gallium/drivers/zink/zink_context.c b/src/gallium/drivers/zink/zink_context.c
index db5cace4754..2c24f2e11b9 100644
--- a/src/gallium/drivers/zink/zink_context.c
+++ b/src/gallium/drivers/zink/zink_context.c
@@ -4367,7 +4367,7 @@ zink_copy_image_buffer(struct zink_context *ctx, struct zink_resource *dst, stru
    if (needs_present_readback)
       zink_kopper_present_readback(ctx, img);
 
-   if (ctx->oom_flush && !ctx->batch.in_rp)
+   if (ctx->oom_flush && !ctx->batch.in_rp && !ctx->unordered_blitting)
       flush_batch(ctx, false);
 }
 
@@ -4497,7 +4497,7 @@ zink_resource_copy_region(struct pipe_context *pctx,
       zink_copy_buffer(ctx, dst, src, dstx, src_box->x, src_box->width);
    } else
       zink_copy_image_buffer(ctx, dst, src, dst_level, dstx, dsty, dstz, src_level, src_box, 0);
-   if (ctx->oom_flush && !ctx->batch.in_rp)
+   if (ctx->oom_flush && !ctx->batch.in_rp && !ctx->unordered_blitting)
       flush_batch(ctx, false);
 }