Manipulating a deformable linear object (DLO) such as wire, cable, and rope is a common yet challenging task due to their high degrees of freedom and complex deformation behaviors, especially in an environment with obstacles. Existing local control methods are efficient but prone to failure in complex scenarios, while precise global planners are computationally intensive and difficult to deploy. This paper presents an efficient, easy-to-deploy framework for collision-free DLO manipulation using mobile manipulators. We demonstrate the effectiveness of leveraging standard planning tools for high-dimensional DLO manipulation without requiring custom planners or extensive data-driven models. Our approach combines an off-the-shelf global planner with a real-time local controller. The global planner approximates the DLO as a series of rigid links connected by spherical joints, enabling rapid path planning without the need for problem-specific planners or large datasets. The local controller employs control barrier functions (CBFs) to enforce safety constraints, maintain the DLO integrity, prevent overstress, and handle obstacle avoidance. It compensates for modeling inaccuracies by using a state-of-the-art position-based dynamics technique that approximates physical properties like Young's and shear moduli. We validate our framework through extensive simulations and real-world demonstrations. In complex obstacle scenarios-including tent pole transport, corridor navigation, and tasks requiring varied stiffness-our method achieves a 100% success rate over thousands of trials, with significantly reduced planning times compared to state-of-the-art techniques. Real-world experiments include transportation of a tent pole and a rope using mobile manipulators. We share our ROS-based implementation to facilitate adoption in various applications.