Only goal difference is currently keeping the Gunners above the dotted line, and they take on a Crystal Palace side that needs just a draw to reach the 40-point mark.
Charged with getting the Gunners back into the Premier League, Emery still has two routes open to that goal having confirmed their place in the semi-finals of the Europa League with victory at Napoli in midweek.
Emery has an incredible record in the competition and Arsenal must therefore be regarded as one of the favourites from the four remaining teams, but their best hope of getting back to the top-tier European competition is still on the domestic front.
Arsenal currently sit fourth in the Premier League table, one point behind Tottenham Hotspur and only above fifth-placed Chelsea on goal difference, with Manchester United a further two points behind.
Chelsea have played a game more than the other three teams in the equation, though, and Arsenal seem to have hit form in timely fashion having lost just one of their last eight league outings.
It is their home form which has propelled them into a position of control, with only Manchester City and Liverpool having picked up more points in front of their own fans this season and Arsenal currently on a run of 10 successive league wins at the Emirates - a streak that stretches back to November.
Arsenal have never won 11 consecutive home top-flight games inside a single season, but they will be big favourites to make that slice of club history on Sunday considering that they have won 30 of their last 31 Emirates league outings against teams outside the established top six - the exception coming against Wolverhampton Wanderers in November.
This weekend may not prove to be a problem, then, but already some fans may let their focus drift to Wednesday's return fixture against Wolves and the trip to Leicester next Monday - both difficult games against top-half opposition which crucially come away from home, where Arsenal have had so many issues this season.
Indeed, the Gunners have picked up twice as many points at home as they have on the road this season - a league-high disparity of 22 points - so they will need to improve that away form significantly if they are to end the season in perfect fashion, which is the only way to guarantee a top-four finish.
Should they manage that then they will break the 80-point barrier for the first time since 2007-08, and they have already surpassed last season's tally with five games still to play.
Those final five games - coupled with up to three in the Europa League - will determine whether Emery's first season in charge is a success or failure, but regardless of whether they make it into the Champions League next term there certainly does seem to have been progress at the Emirates.
Recent Premier League form: WDWWLW
Recent form (all competitions): WWLWWW
Crystal Palace are just a draw away from the 40-point mark, although their Premier League survival is already all but secure with eight points separating them from the relegation zone.
Indeed, the Eagles are now closer to the top half than they are to the bottom three, although breaking into that top 10 is perhaps just out of reach with only four games of their campaign remaining.
Nonetheless it has been a satisfactory campaign for Palace, who are five points better off than at the same stage of last season and could mathematically still post their best-ever Premier League tally.
Roy Hodgson's side have been particularly dangerous on the road, where a league-high 59% of their points have come in a role reversal of Arsenal's home and away fortunes this term.
Palace would sit seventh in the table - above the Gunners - if only away form counted, whereas only relegated Huddersfield Town have posted a worse home record in 2018-19.
The Eagles make the short trip to North London having won three of their last four away league games, and Arsenal will take particular note that they are the only English club to have beaten Man City at the Etihad this season.
What's more, they have also scored an unrivalled 14 Premier League away goals this calendar year, including three at Anfield in January against a Liverpool team that had only conceded three home goals all season prior to that.
There are plenty of reasons for Palace to be optimistic, then, but Hodgson is also hoping to avoid an unwanted personal record of defeats in a Premier League season, having already equalled his tally of 17 from the 2011-12 campaign when he was in charge of West Bromwich Albion.
It remains to be seen whether there will be any fallout from talisman Wilfried Zaha suggesting that he will leave the club in the summer too, and there could be a difficult window coming up for the Eagles with Aaron Wan-Bissaka also thought to be on the radar of the league's biggest teams.
Recent Premier League form: WLWLWL
Recent form (all competitions): LLWLWL
Aaron Ramsey may have played his final game for Arsenal after limping off against Napoli in midweek, although Emery remains hopeful that the Welshman will be able to return before completing his switch to Juventus.
Mesut Ozil looks the most likely candidate to fill in for Ramsey should Emery stick with both Alexandre Lacazette and Pierre-Emerick Aubameyang - the latter of whom has scored an unrivalled six goals in Premier League London derbies this season - up front together.
Sokratis Papastathopoulos is suspended after picking up 10 yellow cards and is expected to be replaced by Shkodran Mustafi in the starting XI, although that too depends on whether Emery once again goes with three at the back.
Palace, meanwhile, will be without Jeffrey Schlupp, who will miss the remainder of the season after picking up an ankle injury against Man City last time out.
Arsenal possible starting lineup:
Leno; Mustafi, Koscielny, Monreal; Maitland-Niles, Torreira, Xhaka, Kolasinac; Ozil; Lacazette, Aubameyang
Crystal Palace possible starting lineup:
Guaita; Wan-Bissaka, Kelly, Dann, Van Aanholt; Townsend, McArthur, Milivojevic, Kouyate, Zaha; Batshuayi
Head To Head
Arsenal have dominated this fixture down the years, winning 28 and losing just four of the previous 44 encounters across all competitions - including just one defeat in their last 18.
Palace have only ever beaten Arsenal twice away from home, and never at the Emirates with their most recent one coming at Highbury in October 1994 - the Eagles' only top-flight away win over the Gunners in 18 attempts.
However, Hodgson's side did hold Arsenal to a 2-2 draw in the reverse fixture and could avoid defeat in both league encounters of a single season for the first time since 1979-80.
We say: Arsenal 2-0 Crystal Palace
This is a fascinating contest between a brilliant home record and an impressive away one, but we are leaning towards Arsenal. Emery's side are on an incredible winning streak in front of their own fans and it is hard to see them slipping up in one of their Emirates outings.