Strong χ⁽²⁾ interactions at low optical powers are key to scalable nonlinear and quantum photonics. Although doubly resonant microresonators exhibit exceptional efficiencies, they require simultaneous resonance and phase matching of widely separated optical frequencies, making them inherently sensitive to fabrication and operating conditions. Singly resonant cavities eliminate this constraint by resonating at only the fundamental frequency while the second-harmonic field propagates in a single pass, but they have traditionally sacrificed nonlinear efficiency. Here, we demonstrate a singly resonant InGaP-on-insulator microresonator that overcomes this tradeoff. Combining the large χ⁽²⁾ nonlinearity of InGaP with high-quality-factor resonators, we achieve efficient and widely tunable second-harmonic generation, broadband quantum-frequency-comb generation, and low-threshold optical parametric oscillation. Unlike conventional centimeter-long singly resonant devices, our millimeter-scale InGaP devices deliver nonlinear performance comparable to, and even exceeding, doubly resonant systems. By overcoming the conventional efficiency-robustness tradeoff of singly resonant devices, this work opens a new route to low-power, broadband, and widely tunable χ⁽²⁾ nonlinear and quantum photonics.