England defender Konsa scrambled home from a corner in the seventh minute at the Emirates Stadium to claim his first goal for the club since arriving from Aston Villa in the summer.
Gabriel sealed victory with a second-half header on his 200th Premier League appearance, ensuring the Gunners took full advantage of City’s 2-1 defeat at Aston Villa in Saturday’s early kick-off.
Victory for Mikel Arteta’s reigning champions was a seventh from eight top-flight fixtures this season and an 11th from 13 games in all competitions.
Everton had opportunities to spring a surprise, with Thierno Barry and Kiernan Dewsbury-Hall wasting their best openings before they slipped to a second-successive defeat.
Arsenal manager Arteta made five changes following Wednesday’s 2-2 Champions League draw away to Bayern Munich, including handing striker Viktor Gyokeres a first league start of the campaign.
The Gunners scored 29 set-piece goals en route to winning the title last season but kicked off having failed to register one this term.
That statistic ended with just over six minutes played on a rainy afternoon in north London.
Amid a succession of corners, Konsa slotted in at the back post after Gabriel’s header into the ground from Martin Odegaard’s right-wing delivery took a deflection and was touched on to the crossbar by Toffees goalkeeper Jordan Pickford.
Everton, who made three changes after their unbeaten start was ended by last weekend’s 2-0 home loss to Chelsea, responded positively.
Midfielder James Garner saw an effort from range gathered by Gunners goalkeeper David Raya at the second attempt.
Raya was then fortunate to escape being punished for a poor punch from a corner after Tyrique George’s strike flicked off Ben White and flashed past the right post.
Gunners winger Noni Madueke twice fired wide at the other end before the Toffees were almost gifted a 44th-minute equaliser.
White’s attempted header back to Raya lacked power but Arsenal survived as Barry’s deft finish was easily saved.
Having lost Bukayo Saka to a quad issue in Munich in midweek, Arsenal were relieved to see key defender Gabriel overcome an injury scare early in the second half.
The Brazil international stayed down after making a clearance before returning to the pitch following physio treatment to secure breathing space in the 68th minute.
Substitute Bruno Guimaraes, who came on as part of a triple change shortly after Arteta was booked for leaving his technical area, slipped in White down the right. The full-back – making his 200th Arsenal appearance – stood up an inviting cross to the back post, where the unmarked Gabriel rose to power into the bottom-left corner.
Everton had won just once on their previous 21 visits to the Emirates.
David Moyes’ side should have set up a grandstand finish but unmarked midfielder Dewsbury-Hall directed a glancing header wide from a Garner cross seven minutes from time and Arsenal comfortably registered a ninth consecutive home success to draw level with City.