Nucleosomal histone H2A is exchanged for its variant H2A.Z by the SWR1 chromatin remodeler, but the mechanism and timing of histone exchange remain unclear. Here, we quantify DNA and histone dynamics during histone exchange in real time using a three-color single-molecule FRET assay. We show that SWR1 operates with timed precision to unwrap DNA with large displacement from one face of the nucleosome, remove H2A-H2B from the same face, and rewrap DNA, all within 2.3 s. This productive DNA unwrapping requires full SWR1 activation and differs from unproductive, smaller-scale DNA unwrapping caused by SWR1 binding alone. On an asymmetrically positioned nucleosome, SWR1 intrinsically senses long-linker DNA to preferentially exchange H2A.Z on the distal face as observed in vivo. The displaced H2A-H2B dimer remains briefly associated with the SWR1-nucleosome complex and is dissociated by histone chaperones. These findings reveal how SWR1 coordinates DNA unwrapping with histone dynamics to rapidly and accurately place H2A.Z at physiological sites on chromatin.