City lost 3-1 at Stirling Albion with Smith striking twice to become the first SPFL player this season to hit 20 goals.
Smith's clinical finishing was the main difference between the teams.
He opened the scoring on nine minutes, working a one-two to go through the visiting defence and slide a left foot shot into the corner of the net.
His second goal was even sharper, a difficult near post finish on the half hour after good work on the right by Ross McGeachie.
City's best chances saw Scott Smith shoot a powerful left foot effort over while defender Cammy Eadie had a header cleared off the line.
The impressive Darren Smith wasn't far away from a hat-trick after a fine turn and shot in the second half.
However Elgin's hopes were ended by a third Stirling goal as Ross Kavanagh's deflected cross looped high into the danger area and home forward Peter MacDonald beat keeper Brett Long in the air to nod home.
Gavin Price's side did score a consolation through Jordan Allan's wickedly deflected drive, but Stirling ran out worthy winners.
The result saw City slip to fifth but they have two consecutive home games now against Annan Athletic this weekend and Montrose the following Saturday.