Cowden could have gone ahead after just four minutes but Liam Buchanan was unable to find enough power to trouble Kieron Renton when he connected with Armand One's cross from the left.
But the home striker opened the scoring in the 16th minute when One nodded on a long ball and Buchanan went in behind the Elgin defence to lob the ball into the net.
Elgin almost equalised five minutes later, but Paul Kaczan blasted just wide from Adam Nelson's free-kick. Buchanan then went close on the half-hour with an effort from the edge of the box, but it was just too high.
Cowden were severely struck by a bout of nerves as the title loomed, and just before the interval Kaczan again went agonisingly close with a glancing header.
But just five minutes after the break the home support sensed the title was in their grasp as One blasted home a loose ball from eight yards.
Howeve, Nelson made Cowden sweat again when he curled home a delightful free-kick in the 69th minute.
Elgin striker Chris Gardiner was sent of for an off-the-ball incident with seven minutes left, but the visitors still look more likely to score until the final whistle eventually brought scenes of joy for Cowden.