Everton made the brighter start of the two and they would be the first to declare themselves unlucky after VAR did not award an early penalty after a cross struck Oriol Romeu’s arm on its way towards the intended target.
But Saints quickly found their footing and came close through James Ward-Prowse, only for Jordon Pickford to deny the world’s best free-kick taker with a finger-tips save.
Pickford would keep the scoreline level when he cleared the ball off his own line in the 32nd minute after Tino Livramento bundled Ward-Prowse’s corner-kick towards goal.
Jan Bednarek then hit the bar with a header, before Kyle Walker-Peters had a clear chance for the breakthrough goal, but fired wide of the post from the edge of the box.
Everton thought they had poached the opening goal shortly after the restart, only for Dominic Calvert-Lewin to be flagged for offside in the build up.
Saints instead made it 1-0 in the 52nd minute following a quick build-up play after Elyounoussi dispossessed Andre Gomes inside the Everton half.
The challenged allowed Romeu to pick up the loose ball and charge towards the box before playing across the line to Che Adams who squared the opportunity to Armstrong to squeeze a shot in at the near post.
Southampton continued to search for the goal that would seal all three points, with Walker-Peters forcing a save whilst Armando Broja slid a shot wide of the target.
Second half substitute Long made it 2-0 to Saints with his first touch of the match seven minutes from full-time when he connected with Livramento’s cross at the back post, calmly heading back across goal.
Saints strengthened their position in the top of half of the table with the win, sitting on 32 points from 25 games—five points ahead of Crystal Palace.
Everton, meanwhile, are being pulled back into a relegation battle having picked up just three points from their last six matches.
Southampton (4-4-2): Forster; Walker-Peters, Salisu, Bednarek, Livramento; Elyounoussi, Romeu, Ward-Prowse, S. Armstrong (Djenepo 90+3); Broja (Long 84), Adams (A. Armstrong 90+1)
Unused subs: Caballero (GK), Diallo, Stephens, Smallbone, Valery, Walcott
Goals: S. Armstrong (52), Long (84)
Everton (4-4-2): Pickford; Kenny, Keane, Holgate, Coleman; Gordon (Alli 75), van de Beek, Allan (Gomes 45), Iwobi (Townsend 65); Richarlison, Calvert-Lewin
Unused subs: Begovic (GK), Rondon, Patterson, Mykolenko, El Ghazi, Branthwaite
Bookings: Allan (15) Calvert-Lewin (40)