State-of-the-art methods for large-scale 3D reconstruction from RGB-D sensors usually reduce drift in camera tracking by globally optimizing the estimated camera poses in real-time without simultaneously updating the reconstructed surface on pose changes. We propose an efficient on-the-fly surface correction method for globally consistent dense 3D reconstruction of large-scale scenes. Our approach uses a dense Visual RGB-D SLAM system that estimates the camera motion in real-time on a CPU and refines it in a global pose graph optimization. Consecutive RGB-D frames are locally fused into keyframes, which are incorporated into a sparse voxel hashed Signed Distance Field (SDF) on the GPU. On pose graph updates, the SDF volume is corrected on-the-fly using a novel keyframe re-integration strategy with reduced GPU-host streaming. We demonstrate in an extensive quantitative evaluation that our method is up to 93% more runtime efficient compared to the state-of-the-art and requires significantly less memory, with only negligible loss of surface quality. Overall, our system requires only a single GPU and allows for real-time surface correction of large environments.