During the last years, hardware accelerators have been gaining popularity thanks to their ability to achieve higher performance and efficiency than classic general-purpose solutions. They are fundamentally shaping the current generations of Systems-on-Chip (SoCs), which are becoming increasingly heterogeneous. However, despite their diffusion, a standard, general solution to manage them while providing speed and consistency has not yet been found. Common methodologies rely on OS mediation and a mix of user-space and kernel-space drivers, which can be inefficient, especially for fine-grained tasks. This paper addresses these sources of inefficiencies by proposing an ISA eXtension for Integrated Accelerator Management (IXIAM), a cost-effective HW-SW framework to control a wide variety of accelerators in a standard way, and directly from the cores. The proposed instructions include reservation, work offloading, data transfer, and synchronization. They can be wrapped in a high-level software API or even integrated into a compiler. IXIAM features also a user-space interrupt mechanism to signal events directly to the user process. We implement it as a RISC-V extension in the gem5 simulator and demonstrate detailed support for complex accelerators, as well as the ability to specify sequences of memory transfers and computations directly from the ISA and with significantly lower overhead than driver-based schemes. IXIAM provides a performance advantage that is more evident for small and medium workloads, reaching around 90¢ in the best case. This way, we enlarge the set of workloads that would benefit from hardware acceleration.