Phil Parkinson had urged his side not to be complacent at bottom side Wednesday, and despite seeing his troops dominate possession from the outset, the best opening early on fell to Owls debutant Jerry Yates, who fired over after combining with Lowe.
After Nathan Broadhead failed to make full contact with a header from close range, Wrexham worked their way into an encouraging position, which ended with Callum Doyle having a shot blocked.
But the first half was devoid of ruthlessness, from both sides, in front of goal – as evidenced when Ben Sheaf volleyed just over in added time after latching on to Doyle’s lofted ball over the top.
The early stages of the second half followed a similar pattern, although the Red Dragons’ quality shone through just before the hour mark.
Max Cleworth threaded through to Issa Kabore, whose cross from the right found Smith and he poked home the opener at the back post with his fourth goal in as many league starts.
Wrexham turned the screw as they went in search of a second goal, with Murphy Cooper denying Smith at his near post as Parkinson’s men dominated.
The Owls were clinging on and were grateful to see Smith guide a further effort wide.
But they had two chances in quick succession as Arthur Okonkwo produced a vital save to deny Cadamarteri before Lowe had a shot cleared off the line from the resulting corner.
After surviving that nervy spell, Wrexham saw out the latter stages with minimal fuss to keep an eighth clean sheet of the Championship season – with the Owls failing to score for a seventh league game running, their worst run since 2005.
