Massive OB stars are critical to the ecology of galaxies and yet our knowledge of OB stars in the Milky Way, fainter than V ˜ 12, remains patchy. Data from the VST Photometric Hα Survey (VPHAS+) permit the construction of the first deep catalogues of blue excess-selected OB stars, without neglecting the stellar field. A total of 14 900 candidates with 2MASS cross-matches are blue-selected from a 42 deg2 region in the Galactic plane, capturing the Carina Arm over the Galactic longitude range 282° ≲ ℓ ≲ 293°. Spectral energy distribution fitting is performed on these candidates' combined VPHAS+ u, g, r, i and 2MASS J, H, K magnitudes. This delivers effective temperature constraints, statistically separating O from early-B stars and high-quality extinction parameters, A0 and RV (random errors typically ˜0.1). The high-confidence O-B2 candidates number 5915 and a further 5170 fit to later B spectral type. Spectroscopy of 276 of the former confirms 97 per cent of them. The fraction of emission-line stars among all candidate B stars is 7-8 per cent. Greyer (RV > 3.5) extinction laws are ubiquitous in the region, over the distance range 2.5-3 to ˜10 kpc. Near prominent massive clusters, RV tends to rise, with particularly large and chaotic excursions to RV ˜ 5 seen in the Carina Nebula. The data reveal a hitherto unnoticed association of 108 O-B2 stars around the O5If+ star LSS 2063 (ℓ = 289.77°, b = -1.22°). Treating the OB star scaleheight as a constant within the thin disc, we find an orderly mean relation between extinction (A0) and distance in the Galactic longitude range, 287.6° <ℓ < 293.5°, and infer the subtle onset of thin-disc warping. A halo around NGC 3603, roughly a degree in diameter, of ˜500 O-B2 stars with 4 < A0(mag) < 7 is noted.