The metaphase-anaphase transition is orchestrated through proteolysis of numerous proteins by a ubiquitin protein ligase called the anaphase-promoting complex or cyclosome (APC/C). A crucial aspect of this process is sister chromatid separation, which is thought to be mediated by separase, a thiol protease activated by the APC/C. Separase cleaves cohesin, a ring-shaped complex that entraps sister DNAs. It is a matter of debate whether cohesin-independent forces also contribute to sister chromatid cohesion. Using 4D live-cell imaging of Drosophila melanogaster syncytial embryos blocked in metaphase (via APC/C inhibition), we show that artificial cohesin cleavage is sufficient to trigger chromosome disjunction. This is nevertheless insufficient for correct chromosome segregation. Kinetochore-microtubule attachments are rapidly destabilized by the loss of tension caused by cohesin cleavage in the presence of high Cdk1 (cyclin-dependent kinase 1) activity, as occurs when the APC/C cannot destroy mitotic cyclins. Metaphase chromosomes undergo a bona fide anaphase when cohesin cleavage is combined with Cdk1 inhibition. We conclude that only two key events, opening of cohesin rings and downregulation of Cdk1, are sufficient to drive proper segregation of chromosomes in anaphase.