Pairing the electrocatalytic hydrogenation (ECH) reaction with different anodic reactions holds great promise for producing value‐added chemicals driven by renewable energy sources. Replacing the sluggish water oxidation with a bio‐based upgrading reaction can reduce the overall energy cost and allows for the simultaneous generation of high‐value products at both electrodes. Herein, we developed a membrane‐electrode assembly (MEA)‐based electrolysis system for the conversion of 5‐(hydroxymethyl)furfural (HMF) to bis(hydroxymethyl)furan (BHMF) and 2,5‐furandicarboxylic acid (FDCA). With (2,2,6,6‐tetramethylpiperidin‐1‐yl)oxyl (TEMPO)‐mediated electrochemical oxidation (ECO) of HMF at the anode, the unique zero‐gap configuration enabled a minimal cell voltage of 1.5 V at 10 mA, which was stable during a 24‐hour period of continuous electrolysis, resulting in a combined faradaic efficiency (FE) as high as 139 % to BHMF and FDCA. High FE was also obtained in a pH‐asymmetric mediator‐free configuration, in which the ECO was carried out in 0.1 M KOH with an electrodeposited NiFe oxide catalyst and a bipolar membrane. Taking advantage of the low cell resistance of the MEA‐based system, we also explored ECH of HMF at high current density (280 mA cm−2), in which a FE of 24 % towards BHMF was achieved. The co‐generated H2 was supplied into a batch reactor in tandem for the catalytic hydrogenation of furfural or benzaldehyde under ambient conditions, resulting in an additional 7.3 % of indirect FE in a single‐pass operation. The co‐electrolysis of bio‐derived molecules and the tandem electrocatalytic‐catalytic process provide sustainable avenues towards distributed, flexible, and energy‐efficient routes for the synthesis of valuable chemicals.