The rapid development in designs and fabrication techniques of superconducting qubits has helped making coherence times of qubits longer. In the near future, however, the radiative decay of a qubit into its control line will be a fundamental limitation, imposing a trade-off between fast control and long lifetime of the qubit. In this work, we successfully break this trade-off by strongly coupling another superconducting qubit along the control line. This second qubit, which we call a Josephson quantum filter (JQF), prevents the qubit from emitting microwave photons and thus suppresses its relaxation, while faithfully transmitting large-amplitude control microwave pulses due to the saturation of the quantum filter, enabling fast qubit control. We observe an improvement of the qubit relaxation time without a reduction of the Rabi frequency. This device could potentially help in the realization of a large-scale superconducting quantum information processor in terms of the heating of the qubit environments and the crosstalk between qubits.