Saka jumped from the bench to put Arsenal 2-0 ahead in Tuesday's 2-1 win against Fulham.
The England winger, following three months out with a hamstring injury, celebrated scoring with Wilson, who was taking in the game from the home dugout.
Afterwards, Gunners manager Mikel Arteta said: "As a manager I'm part of the staff. We all love this kind of recognition and gestures because it goes beyond the professional side of it.
"There is a connection there that is so necessary and to be able to appreciate as well the amount of work, stress and responsibility that they have to go through because they will be like this. I hope everything goes well and the work that we've done is going to work. So, I was very pleased with that.
"That's why the emotional part is so important because you can do all the physical work and all the conditioning but you need to leave the players. Four months is a long time and there are moments that we travel and we go to play Champions League and you are there for two days, you are on your own at the training ground and it's not easy."