City On The Edge Of Forever: Spock uses primitive technology to construct a machine to access the information stored in his tricorder. Genius is genius regardless of surroundings...
The Empath: Spock has the flash of insight that his own resistance to the energy field is what is empowering it.
The Galileo Seven: When all hope is lost Spock chooses to bet all on a desperate act, he jettisons all the remaining fuel to signal the Enterprise, knowing having done so within seconds the shuttlecraft will spiral into the atmosphere and burn up
I don't consider him a rationalist character. He is always hung up about what is logical, as opposed to what is observably right.
Uhura: Mr. Spock, sometimes I think if I hear that word "frequency" again, I'll cry.
Spock: It is illogical for a communications officer to resent the word "frequency."
What kind of answer is that? "Too bad you dislike your job?" A rationalist answer would have been something along the lines of "Can you explain why, maybe we can find out what went wrong with your feelings and find a way to fix them or work them around?"
There is a difference between rationality and smartassery.
Hence "(straw)" in the title. See e.g. this summary of a talk by Julia Galef about the difference between being a Straw Vulcan (memetic hazard warning: TVTropes) and being an actual practitioner of rationality.
[EDITED to link to the LW article that has a transcript of the original talk an a link to the YouTube video.]
Hopefully at least one or two would show a virtue of non-straw rationality.
Episode list