One of the unexpected breakdowns in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for a quantum turbo code to have an unbounded minimum distance and for its iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm gives a theoretical and practical "turbo boost" to these codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties, and simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 5.5 dB beyond that of standard quantum turbo codes. Entanglement is *the* resource that enables a convolutional encoder to satisfy both properties because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. Finally, simulation results demonstrate that interleaved serial concatenation of EAQ convolutional encoders leads to a powerful code construction with excellent performance on a memoryless depolarizing channel.