Matthew Foulds made the breakthrough for the home side at Southport before Evans headed in the second and then wrapped up the victory with a superb free-kick.
The Toffees are now on four points from three matches and move up to second in Group B, above third-placed Watford on goal difference.
See: Everton report
Saints goalkeeper Jack Bycroft saved a penalty from Jaidon Anthony after Dobre's opener, before Scrimshaw put the Cherries top of Group E on seven points, three above their third-placed opponents.
Jake Dunwoody and Gabriel Kyeremateng also netted as Stoke moved into second on five points, while Forest are bottom and winless.
See: Stoke report
A brilliant free-kick from Herbie Kane opened the scoring for the unbeaten Reds, who stay top on seven points.
See: Liverpool report
Stephen Weame opened the scoring and Stephen Walker added a brace, before further efforts from Isaiah Jones and Ben Liddle for Boro.
Josh Shonibare put the Rams in front and Jahmal Hector-Ingram scored twice.
An own goal from Joe Bateman gave Birmingham hope, before Jordan Brown and Jayden Mitchell-Lawson wrapped up the victory.