The Robins had already won twice at the Mettal Stadium this season in the FA Trophy.
But the Kingfishers struck the only goal of this Southern League clash on 82 minutes when Evesham failed to deal with Alfie Bridgman’s deep corner, and Josiah Dunstan was on hand to knock the loose ball over the line.
In a game of few clear-cut chances, Shamar Moore saw an early shot deflected just wide at the near post. Meanwhile Sam Tanner and Roberto Nditi forced saves from Alex Harris.
Callum Smart was called upon more as the game progressed, saving from Levi Steele and Amer Awadh. Deep into injury time the visiting keeper came up for a corner which resulted in a scramble in front of goal but Town eventually got the ball clear and were able to celebrate an important win.
Smart, Z Nditi, Daniel-Spray, Willmoth, Dunstan, Bourne, Tanner, R Nditi, Moore, Thorpe, Bridgman.
Subs on : Matthews, Forde, Slade. Subs unused : Chowdhary