Point-like space target detection (PSTD) is a critical technology for space situation awareness. However, it grapples with challenges arising from intense noise, stray light, and stars resembling targets, making it difficult for existing methods to differentiate between point-like targets and stars. To address these issues, we propose a PSTD framework guided by local target continuity, global background volatility, and multistar topological features. First, we tailor a background estimation approach to minimize noise and stray light while preserving target details. Then, we introduce a novel K-vector-based star angular distance (KV-SAD) voting strategy, which uses multistar topological features to accurately identify key points. Finally, using these identified key points, we apply a fast linear attitude estimator (FLAE) to create a star template matrix and set up redundant windows for separating similarly shaped targets from stars. Extensive experiments across four space image sequences achieved an average AUC( $P_{d}, \tau$ ) of 93.36%, which is 12.79% higher than the best baseline method, showing the best balance between detection rate and false alarm rate. This significant improvement underscores the strong generalization of our novel PSTD framework to diverse and challenging space scenarios.