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Understanding the mode of deformation around the Eastern Himalayan Syntaxis (EHS) is crucial for models of Tibetan Plateau evolution. To constrain rotations and translation east of the EHS, we present new palaeomagnetic data from meta-basalt layers—possibly sills—of the Baoshan Block in western Yunnan, southeastern Tibet Plateau; the meta-basalts were either emplaced or metamorphosed to greenschist facies at ∼30 Ma (40Ar–39Ar whole rock ages). A detailed rock magnetic study—in combination with reflected and transmitted light microscopy—identifies magnetite and Ti-rich titanomagnetite as the main magnetic carriers. Using alternating field demagnetization, we separated well-clustered characteristic remanent magnetizations. A fold test indicates a syn-folding remanence acquisition, supporting an Oligocene magnetization due to evidence for regional Eocene–Oligocene shortening. The tilt corrected overall site mean direction at 30 per cent of unfolding yields declination/inclination = 042.2°/47.0°, corresponding to a clockwise rotation of 35.1° ± 12.7° with respect to stable Eurasia. This denotes an average rotation rate of 1.17 ± 0.42° Myr−1 since ∼30 Ma, ranging at the lower limit of the present-day, GPS-derived rotation rates. We explain the clockwise rotation by tectonic escape of the Baoshan and the Lanping-Simao blocks along the Ailao Shan shear zone. With the onset of shearing along the Chong Shan and Gaoligong Shan shear zones, the Baoshan Block continued its southeastward escape, decoupled from the Lanping-Simao Block between these two major shear zones. Crustal flow could explain rotation and southward escape after ∼20 Ma. [ABSTRACT FROM AUTHOR]