On the night, Arsenal may have ended up making it look routine but, in the long run, this victory away to West Ham United could well have a few important repercussions.
Most obviously and most tellingly, there was Theo Walcott. The winger-cum-wannabe-forward illustrated that he may not be completely egotistical to want a better deal from the club by also showing he still has a lot to offer.
With the game still so tight on 77 minutes, the substitute stretched it until he snapped it open. After Arsenal had spent so long trying to pull West Ham all over the pitch with their passes, Walcott's pace finally gave them one problem too many to deal with.
He wouldn't have been able to use it, of course, without the equally quick thinking of Olivier Giroud. Given how the French striker poked home the equaliser and then crafted the winner, there was a strong feeling that this might have been a bit of a breakthrough game. At the least, his duck in this division is broken and the assists that he had already provided are no longer the only argument he has.
Perhaps most importantly of all, though, there was the manner in which Arsenal came from behind in such a testing fixture to ensure they didn't drop points for the second week in a row. Wenger acknowledged the importance of that afterwards.
"We knew today that a draw was not good enough for us and we went for it. I think we could have lost it as well because [Kevin] Nolan had a very good chance but we did well," Wenger said.
The fact that Per Mertesacker recovered so impressively to prevent West Ham's number-four even getting a shot on target in that second-half instance is also notable.
Because, more than anyone except Andy Carroll, Nolan has come to define the Sam Allardyce approach that is likely to lift an awkward side into the top half of the table. And, after Arsenal failed one test against Chelsea last Saturday, that specific West Ham style offered another, equally important challenge this week.
Although a record of six wins and four defeats in 15 Premier League matches against Allardyce sides means the West Ham manager has never quite been the bogey opponent often presented, it still would have revealed much about Arsenal had they suffered for the second successive week.
Instead, they never really had such trouble. There were only two occasions when an aerial attack caused them problems and even the opening goal came, ironically, through a brilliant piece of Mohamed Diame technical trickery rather than any of Allardyce's templates.
In short, Arsenal's defence responded very well following the supposed reality check of Chelsea. After that game, Gary Neville said that the side lacked a defensive leader. It is worth noting, though, that Mertesacker didn't play in that match and, here, he showed everyone exactly what they were missing: not just height but organisation and assurance.
Wenger was hugely pleased with his team's defensive display. "You can never completely control Carroll for 90 minutes. We had to be good on the second ball. Because, the problem with West Ham is not only Carroll, it's Nolan," he said. "We could have been punished once or twice. Carroll was really up for it, I must say. He tried from the first to the last minute, but we did well."
Carroll's two knock-downs aside, the only real defensive aberration was when Aaron Ramsey got turned for Diame's superb opening goal. Up until the 41st minute, though, Allardyce could speak even more glowingly of his own team's backline.
He said: "We were defending properly in the first part of the game because, although they were difficult to get the ball off, they didn't create much. I was just hoping we'd get in like that but it shows you, when you don't have that protection, what opposition of that quality can do to you."
Certainly, Giroud finally showed his finishing quality. With Lukas Podolski at last fully exploiting the rare area of space that West Ham were offering, the French striker angled his foot expertly to poke the cross past Jussi Jaaskelainen.
For the next 32 minutes, the match was tight and taut. As Santi Cazorla forced a save and Carroll almost forced the ball home, it could have gone either way. Until, finally, the game definitively turned in a moment that encapsulated the difference between the sides.
The instant a typically rehearsed Allardyce attack broke down, Arsenal tore at them in the manner that recalled the most magnificent Wenger sides.
"The second goal was a killer because we were in a fantastic position to score but, because we pick the wrong pass, all of a sudden we're punished," the West Ham manager said. "If you look back to what we were doing at that time, we were threatening Arsenal. Diame flicked the ball around [Carl] Jenkinson, he's free on the left and what we wanted him to do was either the same as the first half and shoot or smash it across. [Instead] he scuffs it. It hits an Arsenal player and it drops. And you can see from where I am we're in trouble because we've loaded the box to try and score. It's a good goal from their point of view because they've exploited the space brilliantly."
And breathtakingly. What was most impressive about Walcott's key goal was the sheer sleekness of it. From Santi Cazorla's economic pass to Giroud's reverse ball and the eventual precise finish, there wasn't a moment's hesitation from first touch to last.
The same, of course, could be said of Cazorla's contribution as a whole. He eventually capped a superb performance and win with a supreme, swerving strike into the top corner. "I think, overall, he was a delight to watch," Wenger said. "He is very influential in our team."
Here, mention should also go to Mikel Arteta as, ultimately, it was the two Spaniards that provided the platform for the likes of Walcott and Giroud to impress and Arsenal's entire approach to prevail.
Allardyce could only hold his hands up as his team gave their best against a very good team. "I'm pleased with our performance, perhaps a bit disappointed we didn't get a draw."
Wenger, however, was thrilled that any dropped points had been avoided. "It was a good test mentally because we were 1-0 down. We started with a lot of questions raised around the team. This season we have now played seven games. The belief is in the squad and we have a chance. Of course, it's down to us week after week now. The spirit is there, the quality is there. It's how consistent we'll be now."
In that regard, the ripple effect from this ultimately rousing win may well go a long way.