The visiting team had missed a series of chances before McInnes made substitutions which paid off in the 79th minute when Wylde, on for Peter Pawlett, set up fellow substitute Scott Vernon, on for Calvin Zola, to drive the ball high past Hibs keeper Ben Williams from the edge of the box.
Wylde wrapped up the points with a breakaway goal in the second of four minutes added time to get his name on the scoresheet for the first time since signing for the Pittodrie club in the summer after leaving Bolton.
Dons boss McInnes said: "Gregg is coming from a difficult place, where for the last 18 months to two years he really struggled.
"He came back to us lacking in confidence a wee bit, he needed an arm round him and needing encouragement.
"But we feel he is a young player who is going to be better and we are trying to work with him to get the performances he is capable of.
"After debating it, we sent him to Newtongrange Star on Wednesday night to play against Hearts Under-20s and he scored a goal and was outstanding in a 5-0 victory.
"He took confidence from that.
"You forget that he is still a young boy even though he played for a couple of decent-sized clubs in Rangers and Bolton.
"He will be feeling good about himself today."
McInnes insists his side more than deserved their win although he admitted having his heart in his mouth "just a bit" in the 86th minute when Jamie Langfield slipped and kicked the ball straight to Hibs substitute James Collins, who curled his shot past the post.
He said: "It was a good performance from start to finish and a performance needed to beat a decent Hibs team in decent form.
"They have a good squad but we showed we have too, the two substitutes came on and scored the goals that mattered.
"Our squad is looking strong after a period of injuries.
"We passed up some opportunities but I thought we brought a confidence to our play.
"We had good awareness and kept knocking at the door and just when you think it is not going to be your day, Scott Vernon came up with a goal fit to win any game and he played his part in Gregg's goal as well."
Hibs boss Pat Fenlon was puzzled as to why his side seemed to lack the "commitment and tenacity" they showed in the 1-1 home draw against Celtic last week.
He said: "I thought Aberdeen played well but I didn't think we were anywhere near where we were against Celtic so it was disappointing.
"We spoke to the players and told them to make sure that the performance levels, commitment and tenacity against Celtic has got to be the same against everybody else.
"I don't know why it was missing. We didn't get about them early enough.
"We let them dictate the game from early on and that caused us problems.
"We changed the shape to or three times but it didn't help.
"But you have to give them credit, I thought they were very good today, they passed the ball well and they worked the ball harder than us to create space.
"We didn't deserve anything out of it so we can't complain too much."
- Sports & Recreation
- Scott Vernon