For efficient feedstock and energy utilization, integrated biorefinery processes are applied to furfural production from bagasse to convert furfural residue into 5-hydroxymethylfurfural (HMF)—an important intermediate building block for the production of various biochemicals. Here, a techno-economic analysis of the integrated processes of furfural and HMF production combined with electricity generation under different scenarios was performed to identify the most suitable process design. Simulations revealed that using the whole bagasse in the biorefinery plant and recycling 50% waste from the HMF production to recover unreacted sugar (scenario 2) achieved the maximum furfural and HMF production with minimum CO2 emission, compared with integrated processes without sugar recycling (scenario 1), with 80% (scenario 3) and 60% biomass (scenario 4) bypassed to the biorefinery, and with a standalone combined heat and power system (scenario 5). Moreover, heat integration improved the efficiency of biorefinery plant (scenario 2), with an energy recovery potential of 71%, leading to the maximum profit at 11% internal rate of return. However, the high operating cost associated with the requirement of solvents and catalysts for HMF production represents the largest cost distribution in the proposed integrated processes. Sensitivity analysis revealed that solvent cost was the most important parameter for economic benefit. In addition, improving technological efficiency in the pretreatment and HMF production phases can enhance product yield, thereby benefiting the profitability of this process.