WordNet sense 1 (let off the hook):

absolve, free

WordNet sense 2 (show to be reasonable or provide adequate ground for):

warrant

WordNet sense 3 (show to be right by providing justification or proof):

vindicate

WordNet sense 4 (defend, explain, clear away, or make excuses for by reasoning):

apologize, excuse, rationalize, apologise, rationalise, excuse