Context. The disk-outflow connection plays a key role in extracting excess angular momentum from a forming protostar. Although indications of jet rotation have been reported for a few objects, observational constraints of outflow rotation are still very scarce. We have previously reported the discovery of a small collimated molecular outflow from the edge-on T Tauri star-disk system in the Bok globule CB 26 that shows a peculiar velocity pattern, reminiscent of an outflow that corotates with the Keplerian disk. However, we could not ultimately exclude possible alternative explanations for the origin of the observed velocity field. Aims. We report new, high angular resolution millimeter-interferometric observations of CB 26 with the aim of revealing the morphology and kinematics of the outflow at the disk-outflow interface to unambiguously discriminate between the possible alternative explanations for the observed peculiar velocity pattern. Methods. The IRAM PdBI array and the 30 m telescope were used to observe HCO+(1–0) and H13CO+(1–0) at 3.3 mm and 12CO(2–1) at 1.3 mm in three configurations plus zerospacing, resulting in spectral line maps with angular resolutions of 3.″5 and 0.″5, respectively. The SMA was used to observe the HCO+(3–2) line at 1.1 mm with an angular resolution of 1.″35. Additional earlier observations of 13CO(1-0) at 2.7mm with an angular resolution of 1.″0, obtained with OVRO, are also used for the analysis. Using a physical model of the disk, which was derived from the dust continuum emission, we employed chemo-dynamical modeling combined with line radiative transfer calculations to constrain kinematic parameters of the system and to construct a model of the CO emission from the disk that allowed us to separate the emission of the disk from that of the outflow. Results. Our observations confirm the disk-wind nature of the rotating molecular outflow from CB 26 - YSO 1. The new high-resolution data reveal an X-shaped morphology of the CO emission close to the disk, and vertical streaks extending from the disk surface with a small half-opening angle of ≈7°, which can be traced out to vertical heights of ≈500 au. We interpret this emission as the combination of the disk atmosphere and a well-collimated disk wind, of which we mainly see the outer walls of the outflow cone. The decomposition of this emission into a contribution from the disk atmosphere and the disk wind allowed us to trace the disk wind down to vertical heights of ≈40 au, where it is launched from the surface of the flared disk at radii of RL ≈ 20–45 au. The disk wind is rotating with the same orientation and speed as the Keplerian disk and the velocity structure of the cone walls along the flow is consistent with angular momentum conservation. The observed CO outflow has a total gas mass of ≈ 10−3 M⊙, a dynamical age of τdyn ≈ 740 yr, and a total momentum flux of ṖCO ≈ 1.0 × 10−5 M⊙ km s−1 yr−1, which is nearly three orders of magnitude larger than the maximum thrust that can be provided by the luminosity of the central star. Conclusions. We conclude that photoevaporation cannot be the main driving mechanism for this outflow, but it must be predominantly a magnetohydrodynamic disk wind. It is thus far the best-resolved rotating disk wind observed to be launched from a circumstellar disk in Keplerian rotation around a low-mass young stellar object (YSO), albeit also the one with the largest launch radius. It confirms the observed trend that disk winds from Class I YSOs with transitional disks have much larger launch radii than jets ejected from Class 0 protostars.