Against the backdrop of high penetration of renewable energy，the carbon emission characteristics of integrated energy systems （IES） are difficult to accurately characterize due to their strong uncertainty，posing a severe challenge to achieving the “dual carbon” goals.To address the challenge of probabilistic carbon flow analysis for high-dimensional complex systems，a stochastic response surface method based on orthogonal Latin hypercube sampling （OLHS-SRSM） is proposed，which is then employed to drive a two-stage low-carbon economic dispatch for IES.In the pre-dispatch stage，OLHS-SRSM efficiently assesses the probabilistic characteristics of node carbon intensity （NCI） under source-load uncertainties by improving the uniformity and orthogonality of sampling points，generating the initial unit output schedule and significantly enhancing computational accuracy and efficiency in high-dimensional scenarios.In the re-dispatch stage，under the constraints of fixed carbon quotas and tiered carbon pricing，the model introduces a carbon emission responsibility allocation mechanism based on the Shapley value method and couples it with low-carbon demand response （LCDR），achieving dynamic correction of NCI and synergistic source-load emission reduction.Case studies on an E39-G20-H6 system incorporating electricity-gas-heat-hydrogen networks in a provincial region demonstrate that：compared to traditional Monte Carlo simulation，the proposed OLHS-SRSM method improves solving efficiency by approximately 72.52% while ensuring an error of less than 2%，effectively overcoming the "curse of dimensionality"； compared to single-stage or other benchmark scenarios，the proposed two-stage strategy，guided by tiered carbon pricing signals and dynamic NCI，can further reduce total system carbon emissions without compromising economic efficiency.These results verify that the proposed model possesses sound low-carbon regulation capability and engineering application potential in environments with high renewable energy penetration.