The 22-year old Australian-born Scottish midfielder netted his first goal since January 11 and his third for the season in the 73rd minute at Vale Park as Crewe moved out of the tier three relegation zone.
Goals either side of the break from Mathias Pogba and Arsenal loanee Chuks Aneke had Crewe two ahead before former Scotland youth international Inman, who is still eligible to represent Australia, extended their lead.
His goal preceded a consolation effort from Tom Pope who pulled one back for Vale in the 76th minute.
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