Asgarov edged the first period after a single throw, but turned on the style in the second, throwing Kudukhov and pushing him off the mat to secure Azerbaijan's first Wrestling gold of London 2012.
Sharifov was the favourite to win gold after winning last year's World Championships and he did not disappoint, seeing off a spirited fight from his opponent to record a 6-1 2-0 win.
Espinal scored a remarkable 37 points en route to the final - far more than any of his rivals - but his inexperience in international finals showed in the showdown.
The Puerto Rican's poor defence allowed Sharifov to throw him twice in the opening period and two simple scores in the second period were enough to seal victory.
Georgia's Dato Marsagishvili and Iranian wrestler Ehsan Naser Lashgari won bronze in the category.