Substitutes Jayden Stockley and Wes Burns were the key to the success as they now look to win a place in the Betfred Cup semi-finals when they take on St Johnstone on Thursday, before Rangers visit Pittodrie for the first time in five years on Sunday.
Stockley headed the second goal and Burns won a penalty for the third, scored by Kenny McLean, after James Maddison scored on his first start to cancel out Kevin Holt’s strike.
McInnes, pictured, said: “Jayden and Wes certainly helped turn the game for us. We found our killer instinct and that was the thing we had been lacking. There has been decent play in the games but we lacked that killer instinct to win.
“We have reminded the players the feeling we’ve got now is why we play and how our weekends should feel – by winning a game.
“It was important to find that killer instinct. We are only six games in and we have only lost once – to Celtic at Parkhead – so there has not been a lot wrong. But the difference between winning games and drawing games is massive. I think it’s down to the standards the players have set that a draw feels like a defeat.
“We are a club that wants to be among things and be competitive. We have not enjoyed a lot of our weekends because it is all about winning and the players needed reminded of that.
“We needed the end product and we got it through Jayden’s goal and Kenny’s penalty.
“I said at the start of the week we wanted six points and we want to get into a semi-final.
“Then it’s a totally different perception or slant than people thought before the game.
“It’s a chance to get ourselves into a position to compete in the league and cups. You probably shouldn’t look at the table until after the first round of games but you can’t help yourself – and it didn’t look good.”
Dundee manager Paul Hartley said: “I don’t think we deserved to lose 3-1. I thought we played well and it was a good game of football. I thought we were comfortable in the second half only to have one lapse in concentration.
“I felt we dealt with their wide players very well. [Cammy] Kerr and Holt dealt well with Hayes and [Niall] McGinn, but just that one moment... And the penalty-kick is not a penalty, he wins the ball.”