The extinct ocean-going plesiosaurs were unique within vertebrates because they used two flipper pairs identical in morphology for propulsion. Although fossils of these Mesozoic marine reptiles have been known for more than two centuries, the function and dynamics of their tandem-flipper propulsion system has always been unclear and controversial. We address this question quantitatively for the first time in this study, reporting a series of precisely controlled water tank experiments that use reconstructed plesiosaur flippers scaled from well-preserved fossils. Our aim was to determine which limb movements would have resulted in the most efficient and effective propulsion. We show that plesiosaur hind flippers generated up to 60% more thrust and 40% higher efficiency when operating in harmony with their forward counterparts, when compared with operating alone, and the spacing and relative motion between the flippers was critical in governing these increases. The results of our analyses show that this phenomenon was probably present across the whole range of plesiosaur flipper motion and resolves the centuries-old debate about the propulsion style of these marine reptiles, as well as indicating why they retained two pairs of flippers for more than 100 million years.