Alexis Sanchez, Laurent Koscielny and Gabriel could all miss Saturday's Wembley clash with Premier League champions Chelsea following a desperately disappointing day for the Gunners at Emirates Stadium, despite their victory.
Following Hector Bellerin's early opener, Koscielny was shown a straight red card for a wild lunge on Enner Valencia and, after Sanchez had doubled the lead, Gabriel was taken off on a stretcher with a left knee injury after an awkward fall.
Sanchez then hobbled off midway through the second half, in what may yet prove a further blow to Arsenal's hopes of salvaging something from their season.
Aaron Ramsey's superb 91st-minute strike at least enabled Wenger's men to finish their league campaign on a stylish note, after Romelu Lukaku had halved Everton's two-goal deficit with a penalty - the Belgian's 25th Premier League strike of the season.
However, after taking their place at European club football's top table in each of the past 19 seasons, Arsenal end 2016-17 in fifth after Liverpool overcame Middlesbrough 3-0 to seal the all-important fourth place. Everton finish seventh in Ronald Koeman's first campaign in charge.
Arsenal were hanging on prior to their third goal, but began the match brightly and were ahead as Mesut Ozil combined with Ramsey and found space on the left byline, where he squared for Danny Welbeck.
The striker somehow contrived to send the ball away from goal from three yards, but his blushes were spared as it fell perfectly for Bellerin to rifle home into the unguarded net.
The Gunners suffered a setback just six minutes later, though, with Koscielny dismissed for his reckless challenge as Valencia raced away down the right.
Koeman introduced Ross Barkley in place of Tom Davies to exploit the extra space available, but within two minutes Arsenal doubled their advantage with another touch of fortune.
Sanchez's shot from outside the box struck Welbeck and, as the Everton defence appeared to stop, the forward had time to tee up Sanchez to tap home with Joel Robles stranded.
Everton looked more dangerous as the interval approached - four players going close in a mad scramble in the 38th minute before Petr Cech made an excellent save to keep out Lukaku's header.
The Belgian sent a weak header straight at Cech soon after the resumption, before Robles excelled with a double save to deny Welbeck and Ozil.
Gabriel then departed on a stretcher to deepen Arsenal's defensive crisis, Per Mertesacker entering the fray for his first action of the season. His first start could well come against Chelsea at Wembley in six days.
Arsenal felt the numbers should have been evened up when Ashley Williams - already booked - escaped a second yellow for a trip on Welbeck and Everton were soon back in it when Rob Holding inexplicably handled Leighton Baines' harmless cross and Lukaku clinically converted the resulting penalty.
Robles denied Ozil and substitute Alex Iwobi but he could do nothing about Ramsey's sublime curling effort in stoppage time as a troubling day for Wenger at least ended on a positive note.
Key Opta stats:
- Everton are now winless in their last 21 away league games against Arsenal, last beating them in London in January 1996 (2-1).
- The Gunners have scored 95 Premier League goals against Everton – more than any club has against another in the competition’s history.
- Danny Welbeck provided two assists in a single Premier League game for only the second time – the other was in April 2012 for Manchester United, also against Everton.
- Laurent Koscielny has been sent off five times since his Premier League debut in August 2010 – no player has been red-carded more in that time (Tom Huddlestone and Younes Kaboul also 5).
- Koscielny’s red card was the second time he’s been sent off in the opening 15 minutes of a Premier League game – the only player to have done so more than once (also sent off after 9 minutes vs Manchester City in 2013).
- The Gunners have conceded 10 penalty goals this season, one of just two sides in Premier League history to ship double figures of goals from the spot (Hull, 11 also this season).