Edge intelligence, which manifests itself as the combination of edge computing and artificial intelligence, has emerged as a promising solution to delivering high-quality and low-latency computing services for many intelligent applications. Oriented toward an Age-of-Information (AoI)-centric edge intelligence system, this paper studies the problem of joint optimization of sampling and model partitioning that minimizes the maximum system response AoI through decision making on the sampling policy and model partition point. We formulate this joint sampling and offloading problem as a combinatorial optimization model that aims at minimizing the maximum system response AoI by determining the optimal sampling policy and model partitioning strategy. We analyze the impact of model partition point on sampling decision in a theoretical manner and, accordingly, establish a sampling rule for making the sampling decision. We propose a cost-effective heuristic algorithm that relies on the sampling rule to explore the AoI-minimized sampling and model partitioning solution to the formulated problem. Experimental results on a real-world edge intelligence system justify the advantage of the joint optimization algorithm in reducing system response AoI.