Determine resistor power rating using data sheet?
The resistor will see that current, but only for a tiny fraction of time. This website will give you an idea why; after filling in it reports the time constant to be 3.3e-8 seconds. (Which is calculated as easy as R times C, which is why it's called RC constant.) That will mean that the resistor will be exposed to high current for too short to heat up, and likely will be fine.