Iwobi scored the Gunners' second on 56 minutes, after Nacho Monreal had opened the scoring in the first half.
Brighton had moments of their own during the game and went close to equalising in the first half when Solly March's shot cannoned off a post.
The result took Arsenal up to fifth in the Premier League, while Albion sit 14th.
Speaking afterwards to www.arsenal.com, Iwobi said: "I wouldn’t say it was comfortable but we made it as easy as we could for ourselves.
"Brighton are a very good team and they made it difficult for us, but it’s a great result to win the game and come out with a clean sheet."
Arsenal goalkeeper Petr Cech said: “It would have been nice to score more goals and have the last part of the game a bit quieter, but everybody did their job and I thought that we had the right attitude to defend the clean sheet and play until the last second.
“As a team, we’re playing really well at the moment. You can see that everybody is doing the job. You can always improve, though, and today we gave away too many balls. We made some rushed decisions, so we can obviously improve that, but as a team the courage is there, the defensive attitude, the offensive work. This is the way to go forward.”
Monreal added: "I was really lucky to score today. We knew that it was going to be a difficult game because they defend with a lot of players and it’s not easy to break them down.
"I was lucky to be there. I scored my second Premier League goal for Arsenal and I was happy to help the team with my goal. The most important thing was that we got the three points and we have to keep going like that."