Two late goals from Aaron Ramsey and Olivier Giroud robbed Everton of their first three points of the season as Arsenal came from 2-0 down to snatch a point.
First half strikes from Seamus Coleman and Steven Naismith had given the Blues a healthy half time lead.
First Coleman nodded past Wojciech Szczesny then, right on half time, Naismith fired low past the Polish keeper to double the lead.
Both sides had further chances and when Ramsey pulled a goal back late on you could feel the nerves around the capacity crowd as the home team flagged in the latter stages.
And substitute Giroud popped up to snatch a draw as he headed past Tim Howard in the final minute of the 90, much to the despair of the Everton players and fans alike.
Martinez had made two changes to the side that had drawn 2-2 with Leicester at the King Power stadium on the opening day, introducing Coleman and Kevin Mirallas to his starting line-up.
The Spaniard was then forced into another reshuffle as Steven Pienaar was forced off following a crunching tackle, Leon Osman stepping in to replace him with less than 10 minutes on the clock.
It was Arsenal who then came within a whisker of opening the scoring. Coleman did well to beat Nacho Monreal to a Mesut Ozil pass but in an attempt to clear his lines he passed straight to Oxlade-Chamberlain 20 yards out. The England man took it on first time, firing a well-struck effort that fizzed wide.
But the Irishman would make up for that misjudgement and then some. When McCarthy was fouled, a quick free-kick was worked to Gareth Barry and his delightful cross to the back post was perfect for Coleman to nod his first goal in front of the Park End.
It was almost two just seconds later as Steven Naismith nodded on a long ball for Mirallas - but the Belgian’s effort trickled agonisingly wide as he poked his shot beyond the advancing keeper.
The visitors went in search of an equaliser but Oxlade-Chamberlain dragged an effort wide.
Mirallas then thundered a free-kick goalwards, prompting muffled cries of celebration as the netting rippled - only for the ball to bounce harmlessly behind for a goal-kick having struck the outside, rather than the inside, of the net.
McCarthy was, typically, doing a brilliant job of rampaging around in midfield, snuffing out any shred of an Arsenal attack.
That provided the perfect platform from which Everton could launch assaults on the counter. And that is precisely how the Blues went two up right on half time.
Possession was won back on the right flank by Phil Jagileka who fed Lukaku ahead of him. The big striker rolled past Mertesacker, skipped down the right and played in Naismith, who deftly rolled the ball under Szczesny.
That first 45 minutes was every bit the 'School of Science'. And so it was fitting that the guests who walked out onto the Goodison turf during the interval were known as the Holy Trinity. Howard Kendall, Colin Harvey and the grandchildren of the late, great Alan Ball received a rapturous welcome on an evening when the Blues on the field did their utmost to emulate their glorious footballing swagger.
In the background, Olivier Giroud was warming up with some intensity and it was the Frenchman who was introduced for the second period, replacing Sanchez.
He fired an early volley over the top of the Everton bar in the half’s opening minutes.
However, it wasn’t for another 20 minutes that Arsenal enjoyed another sniff at goal, and even then Giroud sent his 20-yard drive inches wide of the target.
But the French international was closer with his next chance. Ozil’s pass could have been cut out but found Giroud’s feet, he turned but was denied by a sprawling Howard.
The Blues’ forward play meanwhile wasn’t quite at its previous incisive best but on came McGeady to inject some wizardry into the attacking ranks, Lukaku making way.
The Irishman’s first contribution was cutting back a cross for Naismith to blast over from the edge of the box, then his pass so nearly freed Coleman round the back of Mertesacker.
Just as it looked like the game was beginning to wind down, Ramsey stabbed home from close range to jangle the nerves of Everton and breathe new life into the visitors.
And that proved just the tonic of the Gunners. A cross from the left was headed past Howard by Giroud to even the scores.
It was a result that was harsh on the hosts, especially after Leicester had done similar last week. But the display was a promising one and that could be taken into Chelsea next week.