Morse gathered the ball 45m out and left three tacklers in his wake on a weaving, side-stepping run to score.
That score was the highlight of the hosts' second-half comeback as they turned around an 18-5 interval deficit to claim a 27-21 bonus point victory courtesy of Keelan Giles' two tries, a penalty try and Morse's wonder score.
Cardiff left with just the single bonus point loss after their scores through Owen Lane and Mason Grady.
Ospreys head coach Toby Booth said of Morse: "The boy is quick, right? We know that he is a talent.
He has got great physical capability. You saw that when he played for Wales U20s. He's quick, he can beat people. He would be the first to say he's not the finished product because he's got some rough edges that we are working on."
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