Evans bundled the ball home in the 72nd minute, the Cottagers having taken the lead after quarter of an hour through Tim Ream.
North End grew into the game as the first half went on and bossed the second half, with little seen of the division's leading scorer Aleksandar Mitrovic who was kept in check by Liam Lindsay.
Here are the PNE player ratings, with strong performances from Lindsay, Evans and Ali McCann.
1. Daniel Iversen 7
Beaten early on but not much he could about that. Little to face in regards of shots and commanded his box well when needed. Photo: Dave Howarth/Camerasport
2. Sepp van den Berg 7
Decent performance both in the back three and when switched to wing-back. Helped cut down Fulham’s threat. Photo: Press Association
3. Liam Lindsay 8
Kept dangerman Mitrovic in check tothe extent the Serb’s only effort was when taking a free-kick.Very good display. Photo: Dave Howarth/Camerasport
4. Andrew Hughes 7
Could have got tighter on Ream for the goal but after that was impressive at the back and won the corner for the equaliser. Photo: Press Association