In the pursuit of designing van der Waals magnetic tunneling junctions (vdW-MTJs) with two-dimensional (2D) intrinsic magnets, as well as to quantitatively reveal the microscopic nature governing the vertical tunneling pathways beyond the phenomenological descriptions on CrI3-based vdW-MTJs, we investigate the structural configuration, electronic structure and spin-polarized quantum transport of graphene|2 monolayer(2ML)-CrI3|graphene heterostructure with Ag(111) layers as the electrode, using density functional theory (DFT) and its combination of non-equilibrium Green's function (DFT-NEGF) methods. The in-plane lattice of CrI3 layers is found to be stretched when placed on the graphene (Gr) layer, and the layer-stacking does not show any site selectivity. The charge transfer between CrI3 and Gr layers make the CrI3 layer lightly electron-doped, and the Gr layer hole-doped. Excitingly, the inter-layer hybridization between graphene and CrI3 layers render the CrI3 layer metallic in the majority spin channel, giving rise to an insulator-to-half-metal transition. Due to the metallic/insulator characteristics of the spin-majority/minority channel of the 2ML-CrI3 barrier in vdW-MTJs, Gr|2ML-CrI3|Gr heterostructures exhibit an almost perfect spin filtering effect (SFE) near the zero bias in parallel magnetization, a giant tunneling magnetoresistance (TMR) ratio up to 2 × 104%, and remarkable negative differential resistance (NDR). Our results not only give an explanation for the observed giant TMR in CrI3-based MTJs but also show the direct implications of 2D magnets in vdW-heterostructures.