Higher-dimensional problems (i.e., beyond four dimensions) appear in medicine, finance, and plasma physics, posing a challenge for tomorrow's HPC. As an example application, we consider turbulence simulations for plasma fusion with one of the leading codes, GENE, which promises to advance science on the way to carbon-free energy production. While higher-dimensional applications involve a huge number of degrees of freedom such that exascale computing gets necessary, mere domain decomposition approaches for their parallelization are infeasible since the communication explodes with increasing dimensionality. Thus, to ensure high scalability beyond domain decomposition, a second major level of parallelism has to be provided. To this end, we propose to employ the sparse grid combination scheme, a model reduction approach for higher-dimensional problems. It computes the desired solution via a combination of smaller, anisotropic and independent simulations, and thus provides this extra level of parallelization. In its randomized asynchronous and iterative version, it will break the communication bottleneck in exascale computing, achieving full scalability. Our two-level methodology enables novel approaches to scalability (ultra-scalable due to numerically decoupled subtasks), resilience (fault and outlier detection and even compensation without the need of recomputing), and load balancing (high-level compensation for insufficiencies on the application level).