The former Shrews striker scored 15 minutes into the game, before turning provider for Taylor Richards who secured the points 10 minutes from time.
Josh Vela, Harry Chapman and Shaun Whalley all threatened with early long-range efforts, before a slack pass from Ro-Shaun Williams allowed Okenabirhie to nip in and fire past goalkeeper Matija Sarkic.
Nathaniel Ogbeta struck the crossbar and David Davis went close, as Shrewsbury enjoyed the majority of the play in the first half.
Again they had spells of pressure early in the second period, but Rovers had carried a threat on the break throughout the contest.
Okenabirhie went close to a second 25 minutes from time, before beating Brad Walker to the ball and slipping in Richards.
The Brighton loanee ran clear and slammed the ball home, ending Rovers’ dismal run of five straight defeats.
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