The first complete multicolor CCD light curves and low-resolution spectra of the short-period Am-type eclipsing binary V2787 Ori are presented. The atmospheric parameters of the primary component, including the effective temperature (T), the gravitational acceleration (log g), and the metallicity [Fe/H], are determined as T-eff = 6993 +/- 82 K, log g = 4.10 +/- 0.22 cm/s(2), and [Fe/H] = -0.40 +/- 0.18 dex, respectively. The Wilson-Devinney (W-D) code was used to analyze those BVRcIc light curves, and the photometric solutions of this eclipsing binary were derived for the first time. It was discovered that V2787 Ori is a shallow-contact, total-eclipsing binary with a factor of f = 0.181(+/- 0.077) and an extremely low mass ratio of q = 0.120(+/- 0.002). The primary contributes about 95% luminosity to the total system, and the temperature difference between the two components exceeds 1600 K. This target may be the smallest mass ratio B-subtype system, but it definitely is among the smallest mass ratio B-subtype systems. The temperature of the secondary is determined as 5413 K, while its mass is estimated as M-2 = 0.17(+/- 0.01) M-circle dot. These properties indicate that the binary may undergo a special evolution where the secondary may be the original more massive component and has transferred most of its mass to its companion. We combined our newly determined eclipse times with those collected from the previous literature, and found that the O - C curve of the binary system shows a cyclic variation with an amplitude of 0.0054 days and a period of 17.3 years, which is explained as the result of the light-time effect, due to a third body orbiting around the central binary. The minimal mass of the third body is 0.208 M-circle dot, and the corresponding orbital radius is about 7.24 au. The shallow-contact configuration, the extremely low mass ratio, the evolved components, and the presence of a tertiary component, all make the B-subtype Am-type contact binary a significant target for further investigations.