In the second minute Thatcham were awarded a penalty for a push on Kyle Tooze which was converted by Shane Cooper-Clark.
Evesham then enjoyed a spell of pressure with a free-kick from Kane Simpson going narrowly wide.
But Thatcham doubled their lead on 26 minutes when Tooze raced onto a long ball and slotted low into the corner for a debut goal.
Evesham pulled a goal back through Kane Simpson on 37 minutes with a penalty awarded for handball. Thatcham then held firm for the rest of the half to lead 2-1 at the break.
The Kingfishers were reduced to ten men on 50 minutes following a second yellow for Stu Cattell, but extended their lead shortly after when Kyle Tooze was again fouled in the box, Cooper-Clark calmly putting away his second penalty.
Evesham once again reduced the deficit on 67 minutes with another Kane Simpson penalty after a foul just inside the box.
Evesham were pushing hard for an equaliser forcing a string of corners, but the 10 men of Thatcham dealt with everything that was thrown at them. On 86 minutes Thatcham sealed the points with a break away goal, Scott Rees putting the finishing touch to a good passing move.
There was just time for Thatcham to be reduced to nine men as Jack Alexander received his second yellow card, but the Kingfishers held on for the 3 points.
Team : Rackley; Stanley, Angell, Miller, Cattell; Alexander, Moran, Kelly, Jeacock; Cooper-Clark, Tooze
Subs : Lynch, Tennant, Glover, Helmore, Rees
Attendance: 201
Report by Matt Bateman