The defender, snapped up from Rotherham in the summer, was in the perfect spot to nod in after goalkeeper Marcus Bettinelli failed to deal with at a Matheus Pereira corner.
It was a result that means Albion are now the only side in the Championship who remain unbeaten.
And Ajayi – who netted eight times for the Millers last season – admitted he was delighted to open his account for the Baggies.
"I lost myself for about five seconds after scoring." the Nigerian international said.
"But then I remembered that we could actually go on to win the game so I ran back up the other end and got back in shape as quickly as I could.
"It was an amazing feeling. I’m just really happy to open my account for Albion.
"It’s been a long time coming. But to get it in front of the away fans near the end of the game was a great feeling.
"More importantly it has kept our unbeaten run going."
The result at Craven Cottage means Albion have now come from behind in six of their seven Championship matches.
"That shows the team has got a lot of grit and a lot of determination," Ajayi continued.
"We can ride those waves and come back stronger.
"We were able to hang in against Fulham when they were on top knowing our quality would come through.
"And when we got on top we made the most of it."
Ajayi was part of the Nigeria team that secured a 2-2 draw in Ukraine on Tuesday.
It meant he didn't return to Albion training until Thursday. But the defender made sure he remained in the best possible shape for the Fulham game.
"I feel really good," he added.
"I made sure I got my body in the best possible shape to be able to play.
"I had a good performance for Nigeria on Tuesday and I was able to take that into the Fulham game."