The 18-year-old forward has 23 goals in all competitions for the Toffees Under-18s this term.
The Toffees, who currently top the Under-18 Premier League table, had set up the midweek clash with the Seagulls after a penalty shootout victory over Stoke City.
Paul Tait's charges were impressive from the off against a side which had beaten West Ham and Manchester United to set up the tie and went ahead on 11 minutes.
Michael Collins broke the deadlock for the hosts after exchanging passes with Anthony Gordon before rifling a low effort into the bottom left corner of the Brighton net.
Just a minute later, Ellis Simms dispossessed an opposition defender before gliding towards goal near the byline and curling in a superb shot from a tight angle.
Everton U18s' fortunes in their competitions are in stark contrast to the first team, which is currently floundering in the Premier League under Marco Silva amid much fan criticism.
Some Toffees fans made their feelings known about the youth side on Twitter, with Simms - who scored his 23rd of the season in all competitions - singled out for praise:
Well at least somethings happening at Everton, glad to see the young boys pulling the weight of the club. #COYB All the way!— EvertonsLoyalRoyalNZBlue (@EvertonsLoyal) February 13, 2019
Yet another goal for simms , kids a real talent— mogsy (@mogs157) February 12, 2019
Why isn't simms in the first team yet— M.C ♿♿ (@blueboy200) February 12, 2019
Under 18s showing first team how to zonal mark. Strong defensive performance, impressed by Astley.— Trevor Edwards (@blackrodblue) February 12, 2019
Would the lads be available for a trip to Wales on the evening of February 26?— Matt Siravo (@matt_siravo) February 12, 2019
Get Ellis Simms in first team squad give us something to get excited about— TheProSpartanGamer (@prospartangamer) February 12, 2019
Up next for Tait's side in the FA Youth Cup is a quarter-final trip to West Bromwich Albion.