Aims: Both components of the bright eclipsing binary α Dra have been resolved using long baseline interferometry and the secondary component has been shown to contribute approximately 15% of the total flux ; however, a spectroscopic detection of the companion star has so far been unsuccessful. We aim for a firm spectroscopic detection of the secondary component of α Dra using state-of-the-art spectroscopic analysis methods for very high-quality spectroscopic observations. This will allow the determination of fundamental and atmospheric properties of the components in the system with high precision and accuracy. Methods: To achieve our goals, we use a combined data set from interferometry with the Navy Precision Optical Interferometer (NPOI), photometry with the TESS space observatory, and high-resolution spectroscopy with the HERMES fibre-fed spectrograph at the La Palma observatory. We use the method of spectral disentangling to search for the contribution of a companion star in the observed composite HERMES spectra, to separate the spectral contributions of both components, and to determine orbital elements of the α Dra system. TESS light curves are analysed in an iterative fashion with spectroscopic inference of stellar atmospheric parameters to determine fundamental stellar properties and their uncertainties. Finally, NPOI interferometric measurements are used for determination of the orbital parameters of the system and angular diameters of both binary components. Results: We report the first firm spectroscopic detection of the secondary component in α Dra and deliver disentangled spectra of both binary components. The components' masses and radii are inferred with high precision and accuracy, and are M_A = 3.186 ± 0.044 M⊙, R_A = 4.932 ± 0.036 R⊙, and M_B = 2.431 ± 0.019 M⊙, R_B = 2.326 ± 0.052 R⊙ for the primary and secondary components, respectively. Combined astrometric and spectroscopic analysis yields the semi-major axis of the system, which is ultimately used to derive the dynamical parallax of π = 11.48 ± 0.13 mas, and the distance d = 87.07 ± 1.03 pc to the α Dra system. Evolutionary analysis of both binary components with MESA stellar structure and evolution models suggests the primary is an evolved post-TAMS A-type star, while the companion is a main-sequence A-type star with a convective core mass of M_cc = 0.337 ± 0.011 M⊙. Positions of both binary components in the Kiel- and HR-diagrams suggest a value of the convective core overshooting parameter f_ov well below 0.010 H_p, and we infer the age of the system to be 310 ± 25 Myr. Conclusions: The inferred near-core mixing properties of both components do not support a dependence of the convective core overshooting on the stellar mass. At the same time, the α Dra system provides extra support to hypothesise that the mass discrepancy in eclipsing spectroscopic double-lined binaries is associated with inferior atmospheric modelling of intermediate- and high-mass stars, and less so with the predictive power of stellar structure and evolution models as to the amount of near-core mixing and mass of the convective core.