The Pittodrie side easily dealt with the Dark Blues thanks to braces from Sam Cosgrove and Andrew Considine and a goal from teenager Connor McLennan.
Calvin Miller scored his first senior goal but it could not prevent Dundee sinking back to the bottom of the league.
While still in fourth place prior to tonight’s fixtures, Aberdeen are now on 33 points from 18 games and lie only a point behind leaders Rangers in a tightly packed top end of the table.
McInnes has challenged his players to make it four wins in a row when they face Hearts at Pittodrie on Saturday.
“I’d rather be top but considering where we were, we set ourselves a task and target before Livingston to win all four games,” he said.
“We felt it was important to hit the 36 point mark after 19 games. It’s the halfway stage and it’s normally where we are, on target to break 70 points. We’ve got nine out of nine since Livingston last Tuesday and we try to get the next three on Saturday.”
“I still think we have improved performances in us,” he added. “When you win maybe eight out of ten that’s not bad shooting for any team. In this league this season it’ll be hard to sustain runs.
“Our own game is decent and we looked confident. I still feel we’re winning games without key players. We’ve had to deal with a lot of injuries so January might give us some respite.”
The need for a new striker is not as pronounced as it once seemed. Cosgrove had scored twice by half-time last night to bring his tally to four in three games. He has had his critics but linked well with the industrious Stevie May beside him.
“Sam’s always worked for the team,” said McInnes. “He’s got added confidence, his game is in a good place. He got good service and support. Stevie has had a big part in that. We’ve been searching for that at the top end of the pitch. Ten scored [in our last three games] is really pleasing.”
Dundee manager Jim McIntyre rued more poor defending from his team. “It wasn’t good enough,” he said. “Simple as that. No excuses. We were miles off it. Aberdeen were stronger and quicker and bullied us.
“I said a couple of weeks ago when we went second bottom on goal difference it’s not all about being there in December, it’s where you are in May.”