Coflow scheduling improves data-intensive application performance by improving their networking performance. State-of-the-art Coflow schedulers in essence approximate the classic online Shortest-Job-First (SJF) scheduling, designed for a single CPU, in a distributed setting, with no coordination among how the flows of a Coflow at individual ports are scheduled, and as a result suffer two performance drawbacks: (1) The flows of a Coflow may suffer the out-of-sync problem -- they may be scheduled at different times and become drifting apart, negatively affecting the Coflow completion time (CCT); (2) FIFO scheduling of flows at each port bears no notion of SJF, leading to suboptimal CCT. We propose SAATH, an online Coflow scheduler that overcomes the above drawbacks by explicitly exploiting the spatial dimension of Coflows. In SAATH, the global scheduler schedules the flows of a Coflow using an all-or-none policy which mitigates the out-of-sync problem. To order the Coflows within each queue, SAATH resorts to a Least-Contention-First (LCoF) policy which we show extends the gist of SJF to the spatial dimension, complemented with starvation freedom. Our evaluation using an Azure testbed and simulations of two production cluster traces show that compared to Aalo, SAATH reduces the CCT in median (P90) cases by 1.53x (4.5x) and 1.42x (37x), respectively.