The second period was frantic in front of a vociferous home crowd with Arsenal’s late goals only coming after Dominik Kohr was shown a second yellow card for a cynical foul.
The Gunners, beaten finalists in last year’s Europa League, are top of the early Group F table on goal difference after Standard Liege beat Vitoria in the night’s other game.
English youngsters make their mark in Europe – who are Saka and Greenwood? Relive Thursday’s Europa League action
Manager Unai Emery opted for a mix of youth and experience for the game in Germany, despite it arguably being Arsenal’s toughest test in Group F, and it was their young players who stood out.
Eighteen-year-old Saka, playing for the first team for the first time this season and fifth time in total, was excellent on the left flank, scoring once and setting up the other two goals.
He created Willock’s goal by beating his marker with fine skill in midfield and was the main threat for the Gunners in the first half.
The only criticism was he spurned a number of chances to increase Arsenal’s lead but he silenced those doubts with an emphatic finish from the edge of the area late on.
Willock played as the Gunners most advanced central midfielder and offered a goal threat but also linked play well, notably with a fine driving run in the second half which ended with Martin Hinteregger excellently blocking an Aubameyang shot.
The scoreline flattered Arsenal in the end but the game will be most memorable for the performance of their youngsters.
Defensive issues remain The Gunners came into the game on the back of their disappointing 2-2 draw against Watford, after which their defensive display was heavily criticised as they spurned a two-goal lead.
Although Arsenal kept a second clean sheet of the season, they still looked uncertain at the back and allowed Eintracht 24 shots on goal – seven fewer than the Hornets’ 31 on Sunday.
Arsenal’s deeper midfielders Granit Xhaka and Lucas Torreira failed to control proceedings with the second half end-to-end until Kohr was dismissed.
Eintracht, who reached the semi-finals of the Europa League last season before losing on penalties to Chelsea, lost strikers Sebastien Haller and Luka Jovic to West Ham and Real Madrid respectively in the summer and had either been in their line-up on Thursday, Arsenal’s slack defence may have been punished.
Kostic caused right-back Calum Chambers significant problems but was wasteful, as was AC Milan loanee Silva, who shot well wide in the second half when given another good opportunity.
That said, Martinez, brought in for first-choice goalkeeper Bernd Leno, impressed with key saves in the first half and assured handling when called upon.
Man of the match – Bukayo Saka
Bakayo Saka Saka’s goal was his first in senior football ‘A dream come true’ – reaction Arsenal winger Bukayo Saka: “I’m so happy to score for Arsenal, it’s a dream come true – I have been dreaming of this moment since I was a kid.
“I just want to keep working hard to make sure I can feel this feeling again.”
Arsenal manager Unai Emery: “We knew tonight was going to be difficult, they fell back very deep and caused us problems early on.
“We recovered the ball well and the young players showed the confidence to take their chances.
“Everybody can be happy and continuing in this competition is important, so it was good to get a good win, especially away from home.”
Eintracht coach Adi Hutter: “It’s a bitter defeat for us, because the performance does not reflect that result.
“When it was still 1-0 for Arsenal, we tried to score the equaliser but then conceded another one.
“The important thing is for us to create chances, I have seen enough of those. A goal can help open some doors, give you a boost, that did not happen today.”
Aubameyang’s goal-scoring run – the best stats
Arsenal have only lost one of their 13 group stage games in the Europa League (W10 D2), while this was their sixth consecutive clean sheet in the group stage of the competition.
Arsenal picked up their first European away win against German opposition since November 2013 (1-0 v Borussia Dortmund in the Champions League), having failed to win on any of their previous five trips (D1 L4).
Eintracht Frankfurt suffered their heaviest home defeat across European competitions – in what was their 74th such game on home soil.
Pierre-Emerick Aubameyang has netted seven goals in his last seven Europa League appearances for Arsenal, with four of those coming away from home.
Bukayo Saka is the youngest player to score for Arsenal in the Europa League/Champions League since October 2008, when Aaron Ramsey (17y 300d) netted against Fenerbahce.