Globalization processes are interwoven with economic structures on a worldwide scale, trade playing a central role as one of the elemental channels of interaction among countries. Despite the significance of such phenomena, measuring economic globalization still remains an open problem. More quantitative treatments could improve the understanding of globalization at the same time as helping to form a basis for comparative economic history. In this letter, we investigate the time evolution of the statistical properties of bilateral trade imbalances between countries in the trade system. We measure their cumulative probability distribution at different moments in time to discover a sudden transition around 1960 from a regime where the distribution was always represented by a steady characteristic function to a new state where the distribution dilates as time goes on. This suggests that the rule that was governing the statistical behaviour of bilateral trade imbalances until the 1960s abruptly changed to a new form persistent in the last decades. In the new regime, the figures for the different years collapse into a universal master curve when rescaled by the corresponding global value of gross domestic product. This coupling points to an increased interdependence of world economies and its onset corresponds in time with the start of the last wave of globalization.