The visitors started confidently with Kofi Anoyke-Boadi a threat down the left.
But gradually Thatcham took control, as Harry Hoath skipped through on goal but rolled his shot wide.
Town opened the scoring on 25 minutes when Josh Blackwood headed home Kyle Daniel-Spray’s corner.
Just before the break Christian Johnson headed wide at the near post, while David Nyarko almost rounded off a flowing move but the ball deflected just wide.
After the interval Town struck the crossbar twice, as first Daniel-Spray’s cross was tipped on to the bar by keeper Roraigh Browne, then substitute Sam Tanner’s shot was deflected against the woodwork.
For the visitors, Reece Cameron curled a free-kick just wide for the visitors, then Riccardo Alexander-Greenaway’s shot was saved by Toby Fisher.
But with five minutes remaining Daniel-Spray seized on to a loose ball and fired a low 25-yard shot into the corner to seal the points.
The heavens opened in the closing stages and the visitors ended with ten men after Luke Tingey was unable to continue, as Thatcham saw the game out to earn an important three points.
The game was preceded by a minute's applause for former committee member John Haines, who sadly passed away recently.
TEAM : Toby Fisher, Tinashe Gwavava, Kyle Daniel-Spray, Callum Willmoth, Josh Blackwood, Curtis Angell, Jordan Brown, Nathan Jones, Christian Johnson, David Nyarko, Harry Hoath.
Subs on : Sam Tanner, Mo Ceesay, Jordan Alves
Subs unused : Owen Clark, Levi Heholt