Screening for ocular diseases, such as glaucoma and keratoconus, includes measuring the eye-globe intraocular pressure (IOP) and corneal biomechanical properties. However, currently available clinical tools cannot quantify corneal tissue material parameters, which can provide critical information for detecting diseases and evaluating therapeutic outcomes. Here, we demonstrate measurement of eye-globe IOP, corneal elasticity, and corneal geometry of in situ porcine corneas with a technique termed applanation optical coherence elastography (Appl-OCE) with single instrument. We utilize an ultrafast phase-sensitive optical coherence tomography system comprised of a 4X buffered Fourier domain mode-locked swept source laser with an Ascan rate of ~1.5 MHz and a 7.3 kHz resonant scanner. The IOP was measured by imaging the response of in situ porcine corneas to a large force air-puff. As with other noncontact tonometers, the time when the cornea was applanated during the inwards and outwards motion was correlated to a measure air-pressure temporal profile. The IOP was also measured with a commercially available rebound tonometer for comparison. The stiffness of the corneas was assessed by directly imaging and analyzing the propagation of a focused micro air-pulse induced elastic wave, and the corneal geometry was obtained from the OCT structural image. Our results show that corneal thickness decreased as IOP increased, and that corneal stiffness increased with IOP. Moreover, the IOP measurements made by Appl-OCE were more closely correlated with the artificially set IOP than the rebound tonometer, demonstrating the capabilities of Appl-OCE to measure corneal stiffness, eye-globe IOP, and corneal geometry with a single instrument.