It took only four minutes for the hosts to break the deadlock, although they profited from the Seagulls haplessly giving the ball away in their own area, with Iwobi intercepting Bart Verbruggen’s pass and slotting into an empty net.
Shortly after, Rodrigo Muniz nodded wide from near the penalty spot, before Bernd Leno came to the rescue at the other end as he scurried across his line to expertly save Simon Adingra’s point-blank range effort.
Fabian Hürzeler’s side were beginning to click into gear, although they were still searching for that cutting edge in the final third.
Watching from the stands, the boss was left frustrated as his side failed to forge an opening from a string of corners, and they were nearly made to pay when Muniz climbed highest in the box to meet another cross, only to head wide for a second time.
Harry Wilson then sent a volley wide just 10 seconds into the second half, as the Cottagers executed a well-worked kick-off routine.
Minutes later, Jan Paul van Hecke should have done a lot better for the visitors with a header that went over the bar, but they did not have to wait long for the equaliser, as Carlos Baleba levelled by smashing João Pedro’s inviting knock-down into the far corner from 20 yards.
That should have swung the momentum in Brighton’s favour, but Fulham – who have now scored in a club record-equalling 13 successive PL games – had other ideas.
They looked by far the more likely team to find a winner, enjoying particular success down their left flank, although numerous crosses were cleared.
Indeed, it eventually took an own goal to put Marco Silva’s side back in front, as Andreas Pereira’s corner clattered into Matt O’Riley’s back and deflected into the far corner.
There was more to come from the hosts as well, as Iwobi wrapped up a well-deserved victory when wriggling into space in the box and driving a low effort across Verbruggen and into the far corner.
The results leaves the Cottagers unbeaten in nine head to heads, whereas the visitors – who have now only kept one clean sheet in their last dozen outings – missed out on the chance to move back above Manchester City and into the top four.