Autonomous underwater inspection of submerged pipelines is challenging due to confined geometries, turbidity, and the scarcity of reliable localization cues. This paper presents a minimal-sensing strategy that enables a free-swimming underwater robot to center itself and traverse a flooded pipe of known radius using only an IMU, a pressure sensor, and two sonars: a downward-facing single-beam sonar and a rotating 360 degree sonar. We introduce a computationally efficient method for extracting range estimates from single-beam sonar intensity data, enabling reliable wall detection in noisy and reverberant conditions. A closed-form geometric model leverages the two sonar ranges to estimate the pipe center, and an adaptive, confidence-weighted proportional-derivative (PD) controller maintains alignment during traversal. The system requires no Doppler velocity log, external tracking, or complex multi-sensor arrays. Experiments in a submerged 46 cm-diameter pipe using a Blue Robotics BlueROV2 heavy remotely operated vehicle demonstrate stable centering and successful full-pipe traversal despite ambient flow and structural deformations. These results show that reliable in-pipe navigation and inspection can be achieved with a lightweight, computationally efficient sensing and processing architecture, advancing the practicality of autonomous underwater inspection in confined environments.