Spin relaxation, a defining mechanism of nuclear magnetic resonance (NMR), has been a prime method for determining three-dimensional molecular structures and their dynamics in solution. It also plays key roles for contrast enhancement in magnetic resonance imaging (MRI). In bulk solutions, rapid Brownian molecular diffusion modulates dipolar interactions between a spin pair from different molecules, resulting in very weak intermolecular relaxations. We show that in fluids confined in nanospace or nanopores (nanoconfined fluids) the correlation of dipolar coupling between spin pairs of different molecules is greatly enhanced by the nanopore constraint boundaries on the molecular diffusion, giving rise to an enhanced correlation for the spin pair. As a result, the intermolecular dipolar interaction behaves cooperatively, which leads to a large intermolecular dipolar relaxation rate and opposite in sign to the bulk solution. We found that the classical NMR relaxation theory fails to capture these observations in a nanoconfined fluid environment. Hence, we developed a formal theory and experimentally confirmed that enhanced correlation and cooperated relaxation are ubiquitous in nanoconfined fluids. The newly discovered phenomenon and the developed NMR method reveal new applications in a broad range of synthesized and naturally occurring materials in the field of nanofluidics to study molecular dynamics and structure as well as for MRI image enhancement.