Differentiating between a salvageable Ischemic Penumbra (IP) and an irreversibly damaged Infarct Core (IC) is important for therapy decision making for acute ischemic stroke (AIS) patients. Existing methods rely on Computed Tomography Perfusion (CTP) or Diffusion-Weighted Imaging-Fluid Attenuated Inversion Recovery (DWI-FLAIR). We designed a novel Convolutional Neural Network named I2PC-Net, which relies solely on Non-Contrast Computed Tomography (NCCT) for the automatic and simultaneous segmentation of the IP and IC. In the encoder, Multi-Scale Convolution (MSC) blocks were proposed to capture effective features of ischemic lesions, and in the deep levels of the encoder, Symmetry Enhancement (SE) blocks were also designed to enhance anatomical symmetries. In the attention-based decoder, hierarchical deep supervision was introduced to address the challenge of differentiating between the IP and IC. We collected 197 NCCT scans from AIS patients to evaluate the proposed method. On the test set, I2PC-Net achieved Dice Similarity Scores of 42.76 ± 21.84%, 33.54 ± 24.13% and 65.67 ± 12.30% and lesion volume correlation coefficients of 0.95 (p < 0.001), 0.61 (p < 0.001) and 0.93 (p < 0.001) for the IP, IC and IP + IC, respectively. The results indicated that NCCT could potentially be used as a surrogate technique of CTP for the quantitative evaluation of the IP and IC.