A late goal by substitute Charlie Austin gave relegation-threatened Southampton a thrilling 3-2 victory over Arsenal on Sunday in new Austrian manager Ralph Hasenhuettl's first home game.
It was the Londoners' first defeat in 23 games and meant they lost ground on fourth-placed Chelsea, while Southampton moved out of the bottom three.
Danny Ings, back after injury, headed two fine goals in the first half from equally good crosses by Matt Targett and Nathan Redmond.
In between, Mkhitaryan drew Arsenal level with a header of his own and early in the second half he scored via a big deflection.
Yet in the 85th minute Austin, who had come on for the tiring Ings, headed in a cross by Shane Long.
A first win in 13 league games since September 1 sent Southampton above Burnley into 17th place while Arsenal, who had last lost to Chelsea in the Premier League in August, remained fifth in the table.
Unai Emery's team had Laurent Koscielny starting in defence for the first time this season but they were uncertain at the back from the first to last minute against a side that at one stage this season went five league games without scoring.
Koscielny was at fault in failing to cut out Targett's cross from the left and losing Ings, who scored his first headed goal for three years.
The visitors briefly looked more composed and drew level when Nacho Monreal cut back a cross for Mkhitaryan to head in, and a minute later Pierre-Emerick Aubameyang was only denied by a late interception from Jan Bednarek.
Southampton went ahead again, however, before the interval. Redmond supplied the chance with a neat chip and once again Ings eluded his marker to score.
So Arsenal maintained their dismal record of never having been ahead at halftime in the Premier League this season.
As a consequence Emery made one of his regular halftime substitutions in sending on Alexandre Lacazette for wing back Hector Bellerin, and Aubameyang almost equalised within a minute.
Mkhitaryan's second goal was fortunate in the extreme, his shot taking a big deflection off Jannik Vestergaard to leave goalkeeper Alex McCarthy helpless.
Long, replacing Redmond, had a goal rightly disallowed for offside but then picked out Austin with a cross that goalkeeper Bernd Leno failed to deal with.
Chelsea consolidate top four spot
Chelsea consolidated fourth place in the Premier League with a 2-1 win at Brighton & Hove Albion on Sunday that became harder work than had seemed likely in the first half.
Having won 4-0 at the Amex Stadium last season, they were on course for a repeat after taking a 2-0 lead at the interval.
Eden Hazard set up the first goal for Pedro after 17 minutes and scored the second himself before halftime following a defensive error.
Brighton came back into contention through Solly March's goal midway through the second half and Lewis Dunk went close to an equaliser.
The home side have not beaten Chelsea in any competition since 1933 but they stayed 13th in the table, nine points clear of the bottom three places.
Chelsea moved three points clear of London rivals Arsenal, who were beaten at Southampton.
Hazard, who had been outstanding when scoring twice in the 4-0 January win, made the opening goal with his ninth assist of the season.
Regaining possession after his shot was saved, he played a perfect pass to give Pedro a tap-in.
Brighton contributed to their own downfall 12 minutes from halftime with a poor clearance by Leon Balogun.
Willian intercepted and from his own half sent Hazard through to beat goalkeeper Mat Ryan.
From a position of apparent comfort, Chelsea came under pressure after Marcos Alonso had crashed a shot against the post.
The home team revived, halving their deficit when Bernardo headed back across goal for March to score, but Chelsea held on for an important win.