Five days after a memorable triumph at Old Trafford, Roberto Martinez's side maintained their high standards against the Premier League leaders and fully merited their point.
In a game of few clear-cut chances, the Gunners eventually opened the scoring after 80 minutes, as Mesut Ozil nodded home Theo Walcott's clever header.
Gerard Deulofeu rescued a point four minutes later with a fierce strike, following fine work from Ross Barkley and Bryan Oviedo.
Here's a look at some Everton-related talking points to emerge from this contest.
Everton dominated their hosts during an impressive opening 39 minutes.
During that time they made 264 passes to their opponent's 122, managed five shots and—crucially—prevented Arsenal from firing off a single strike at goal.
Steven Pienaar's narrower role was especially key to this. The South African left Carl Jenkinson unsure of when to track him and freed up space for Bryan Oviedo to overlap. It was no surprise that Oviedo and Pienaar exchanged more passes than any other players during the first half.
This opening spell was completely controlled by the Toffees, something Martinez would have undoubtedly enjoyed. However, while this reduced the chances of Everton losing, Arsenal were never truly exposed.
Sitting deep is a better way of stifling Romelu Lukaku, and the Gunners did a good job of slowing the tempo and eventually crowding the visitors out.
Arsenal then had more penetration in the final six minutes than the Toffees had at any time during the first half, highlighting how areas of Martinez's approach still need adjusting to.
At the same time, such an authoritative spell against the Premier League leaders show a glimpse of its full potential.
As Arsenal wrestled back the control, Everton found themselves working harder in defence, but they also found more freedom in the final third, allowing them to test Wojciech Szczesny more often.
However, playing on the break allows a slicker element to the Toffees' game, which makes them far more dangerous.
Several players fit this style, and if an opening goal can be found early, Everton are ideally suited to regularly dissect their opponents on the break—as was evident in the recent 4-0 win over Stoke City.
Ross Barkley was subdued against Manchester United; his passing was a little sloppy, and his final ball became especially wayward.
However, he returned to form in a big way at the Emirates, igniting several breaks with some intricate passes and clever movement.
In front of the watching Roy Hodgson, Barkley recorded more shots (3), created more chances (3) and dribbled around more opponents than any Everton player (3).
He roamed between the channels, drifting wider to create overloads, and occasionally dropped deeper to boost midfield. His quick feet saw him ghost past several challenges in his second impressive performance at the Emirates.
As with any player just turning 20, his form will fluctuate, but this game is more evidence of his considerable potential and shows exactly why he must be persevered with.
Tim Howard struggled for form last season, making several costly errors in late 2012.
Twelve months on and the American has produced some of his best performances in an Everton jersey, making several key contributions to the Toffees' impressive start.
He's recorded eight clean sheets in 15 games, prolonging some overdue form from late last season. In total, he's made 14 clean sheets in his previous 24 Premier League games, compared to just four in the 27 matches before that.
While he wasn't able to prevent Arsenal from scoring, he was once again central to the final result, making four key saves—including two vital one-on-ones—and all without his beard!
James McCarthy and Gareth Barry were two of Everton's leading performers in this game, as they have often been since arriving at the club.
Their introduction to the Toffees' midfield axis has been one of the main reasons Martinez's approach has started to click.
Against some of Europe's finest, both players kept Arsenal quiet early on and made several timely interventions as their opponents upped the ante.
A slight negative is that McCarthy collected his fifth booking of the season, meaning he will miss the home game with Fulham.
Leon Osman will presumably take his spot, but he will need to be quicker on the ball and more forceful in the challenge to adequately fill the void.
Getting four points from Old Trafford and the Emirates is a return every club would take, especially with identical line-ups used in the space of just five days.
Everton have impressed at the start of the Christmas period, negotiating their toughest fixtures, but must now capitalise on a run of less daunting games to boost their quest for Europe.
The first half demonstrated the trouble lesser teams will pose the Toffees, especially at Goodison Park.
While the game was controlled, few chances were created, and improvements must be made to convert these passages into clinical spells that bring an early opening goal.
Already boasting their second-best start in Premier League history, this performance confirms the Toffees can once again compete for the Champions League this season.
Statistics via WhoScored?