B737 Captain reported aircraft breakaway during pushback. Captain applied brakes to stop aircraft.

Narrative

On pushback after I commanded push to the north line off of gate XX; the ground crew stopped aircraft and commanded set brakes. All communication was standard; but I queried the push driver about the aircraft's position. The jet was stopped facing NNE versus W toward ramp Spot X. The driver said he'd push us wherever we needed to go. I queried the ramp controller and he said our current position was a non-standard push. The ramp controller cleared us to continue the push facing W on the north line. I communicated these instructions verbally to the push driver and asked if he was ready for brake release. He responded in the affirmative and I announced (with intentional emphasis) the standard brakes released callout via the interphone. Shortly after the aircraft began moving; there was some unusual towbar sounds and the driver announced the breakaway. The brakes were applied and the aircraft stopped. The parking brake was set; we asked for MX (Maintenance); we advised ramp; and shut the running engine down. The FAs and passengers were routinely updated; and the dispatcher was notified by telephone. MX coordinated with local techs to remove the towbar and complete the required inspections. No damage noted and the new release arrived quickly.