Barnstaple Town were beaten 3-1 by the Robins, who came from behind to take all three points.
A lively end to the first half saw Stephen Reed give Barnstaple the lead with a free-kick from 25 yards, but it was quickly cancelled out by a good finish from Kye Simpson.
Substitute Tyrone Tucker-Dixon put the visitors ahead with 15 minutes of the match remaining with a low finish past Rob Holmes.
Archie Haskayne sealed victory for Evesham in the second minute of stoppage time with a driven shot from 25 yards.
The result means not much has changed for Barnstaple, who remain second from bottom.
Evesham were forced to change from Plan A inside five minutes, with Cory Simpson brought on to replace the injured Adam Page.
Both sides were limited in creating opportunities until the first half came alive in its final 10 minutes.
Before then Holmes had produced a good save to deny Stephen Davies after 18 minutes, while Barnstaple saw a Tallan Mitchell free kick and an effort from Steve Holland denied by Andrew Hannah.
The hosts applied more pressure and were eventually rewarded with five minutes of the half remaining.
Evesham may have felt blessed to still have a full compliment of players on the pitch, with Shane Anson booked for kicking through Harry Stevens, and goalkeeper Hannah shown a yellow for taking out Steve Holland 25 yards from goal.
Barum were aggrieved referee Craig Scriven had blown up before they could have a pop at the empty goal, but Reed ensured they were given some retribution by scoring the resulting free kick with his effort striking the underside of the crossbar before crossing the line.
The hosts lead only lasted five minutes though, with Simpson equalising in the first minute of stoppage time. Holmes had produced an excellent save to deny Davies, but there wasn’t a lot he could do about the follow up, which saw Simpson drive the ball low into the bottom corner from the edge of the penalty area.
Barnstaple began the second half well, with Stevens just off target minutes after the restart. A driven ball into the box from Reed forced Hannah to make a low save after it took a deflection.
Holmes was on form at the other end too, stretching out to touch an effort from Tucker-Dixon from the edge of the penalty area around the post.
It was Tucker-Dixon who would give Evesham the lead with 15 minutes remaining, firing a shot under Holmes after being played in by Davidge.
Barnstaple kept going, with another Reed free kick drawing a reaction stop from Hannah, and a glancing header from Jack Rice-Lethaby held by the keeper.
Haskayne made sure of the result for Evesham, driving a low shot into the bottom corner from 25 yards in the second minute of stoppage time.
Barnstaple Town: Holmes, M Humphreys, Dart (Slough 89), Dardner, Reed, Jones (Middleton), Reay, Holland, Nancekivell, Mitchell, Stevens (Rice-Lethaby 70). Subs not used: Darragh, Darch.
Evesham United: Hannah, Hancock, Tunnicliff, Turley, Anson, Wellow, Thomas (Davidge 70), Haskayne, Simpson (Tucker-Dixon 50) , Davies, Page (Simpson 6). Subs not used: N Humphreys, Harding.
Report Courtesy of North Devon Gazette.