It took just six minutes for Lacazette to convert from Mkhitaryan's attempted shot and the latter turned home the dangerous Alex Iwobi's assist at Emirates Stadium on Sunday.
Lacazette wasted a couple of golden opportunities to stretch the lead before half-time and, while Arsenal's tempo noticeably dropped after the break, Unai Emery's side were in complete control.
Nathan Redmond failed to capitalise on lax Arsenal defending when shooting straight at Bernd Leno one-on-one and shortly afterwards the Gunners went in front.
Iwobi's left-wing cross travelled across the box, with Lucas Torreira seemingly felled by Jack Stephens in his bid to meet the ball, and Mkhitaryan's cross-cum-shot was cleverly flicked in by Lacazette.
It was 2-0 after 17 minutes as goalkeeper Angus Gunn was played into trouble by Stephens and Iwobi pounced on his hasty clearance before squaring for Mkhitaryan to side-foot home from the edge of the box.
Lacazette wastefully blasted over from six yards shortly before the break, while James Ward-Prowse fired wide on the volley for Southampton from Granit Xhaka's wayward pass early in the second half.
The chances began to dry up, although substitute Pierre-Emerick Aubameyang forced a great late save from Gunn, and the only slight concern for Emery was the sight of Iwobi struggling with a calf problem 15 minutes from the end.
What does it mean? Gunners apply top-four pressure
With United drawing against Liverpool and Chelsea featuring in the EFL Cup final, Arsenal stole a march in the race for fourth. Saints, meanwhile, remain 18th and one point shy of safety.
Oh Mkhi you're so fine…
It really was difficult to choose a standout performer for Arsenal. Iwobi had a hand in both goals, while Aaron Ramsey pulled the strings in midfield. But Mkhitaryan finished with an assist – albeit a lucky one – and a strike of his own. He had Southampton worried every time he had the ball.
Slack Stephens sums up sorry Saints defending
Stephens had a tough outing, almost giving away a penalty before Lacazette scored and finding himself in trouble prior to Arsenal's second. Southampton have not won an away league fixture at the Gunners since 1987 and if they continue to defend like this that will not change any time soon.
Key Opta facts
- Arsenal are unbeaten in their last 24 home league games against Southampton (W18 D6) since a 1-0 loss in November 1987.
- Southampton have won none of their 20 away Premier League games against Arsenal (D5 L15) – the most a team has played away at another without ever winning in the competition.
- Since losing 2-0 against Manchester City on the opening weekend, Arsenal have remained unbeaten in 13 Premier League home games (W11 D2), winning the last seven in a row.
- Henrikh Mkhitaryan has been directly involved in each of Arsenal's four Premier League goals against Southampton this season (three goals, one assist).
- Alexandre Lacazette is the first Arsenal player to score in four consecutive Premier League games since Robin van Persie in March 2012 (five games).
Arsenal's top-four bid continues against Bournemouth in midweek before the small matter of Saturday's north London derby. Southampton face a huge home fixture with relegation rivals Fulham on Wednesday.