It wasn't so much to "save face" but more to avoid prosecution and jail time.
Once the Tape was made public any chance of Nixon beating the impeachment charges evaporated, had the impeachment happened He would have been removed and criminal charges filed.
His resignation and pardon was in essence a "plea deal" to avoid going to jail.
Behind watergate, Nixon is best known for starting relations with China which is kind of ironic considering the situation with the current pandemic.
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