Thermal transport in nanoscale two-dimensional (2D) materials is of great scientific interest and has practical implications for energy related applications like thermal management of energy devices, composite battery materials and on-board thermoelectric power generation for sensors. The abilities to manipulate thermal transport in 2D materials is thus highly desirable for future nano energy technologies. In this work, we identify a general rule for controlling the thermal transport in 2D pentagonal materials through bond saturation. We use first-principles calculations to investigate the phonon properties of a series of pentagonal materials, including penta-graphene (PG), hydrogenated PG (h-PG) and fluorinated PG (f-PG), and find that the bond saturation of the carbon atoms through functionalization can reduce the bond anharmonicity and thus increase the phonon lifetime. We can follow this rule to predict very high thermal conductivity of other pentagonal structures with saturated bonds, including penta-CN2 (1027W/mK) and two three-dimensional counterparts of PG called T12-carbon (819W/mK) and AA T12-carbon (1049W/mK). Moreover, similar trend of bond saturation-induced thermal conductivity enhancement can be found in other 2D pentagonal materials, such as penta-SiC2 and penta-SiN2. The results from this work unveil a general bonding-thermal transport relation for 2D materials, which can provide important guidance for designing novel materials with desirable thermal transport properties for energy applications.