It was a result which proved something of a turnaround for Arsenal, who have won three and drawn 0-0 at Chelsea since their Anfield humiliation.
"3 Points, Clean Sheet And A Goal.Perfect Way To Celebrate Independence Day #BIG17", Iwobi tweeted on Sunday.
It was Nacho Monreal who scored a rare goal in the 16th minute to put the Gunners ahead and while Solly March came very close to restoring parity in the 23rd minute, it was not to be.
Arsenal do not even play the best football any more, always a slight consolation to fans when other, more functional teams collected the bigger prizes.
Arsenal is six points behind the Manchester pacesetters of City and United, but things aren't looking as bleak as they did for Wenger in the opening weeks of the season.
"Our last global break was a nightmare, this one is a bit better", he said.
Meanwhile, Wenger challenged Iwobi to provide 10 goals and 10 assists this season after his 56th minute goal against Brighton.
Fottball: Arsenal on a roll, but Liverpool are muddling along
The summer saw Wilshere change his profiles on social media to "professional athlete" and drop any mention of Arsenal, prompting speculation that he was to be the next star to walk away from Arsène Wenger on a free transfer.
'They've got the class, they've got the skill, they've got everything, but they work hard at the same time - that's what makes them world class.
He added: "I knew that after the game at Liverpool everybody did write us off".
Brighton boss Chris Hughton reflected on a Premier League defeat at Arsenal and said: "There were more positives than negatives".
Brighton started well with neat passing but Alexandre Lacazette hit the post in the second minute and Sanchez could not tap in the rebound.
"I would have loved to continue to play but we can not do anything about that".
Not a bad ratio, however it is questionable if he will provide the firepower to help keep the club in England's top division.
And Arsenal reportedly hope they can reach a deal with the player, who joined the North London club when he was nine, by the end of the year.