The teenager, on loan from Norwich, curled a 90th-minute free-kick into the top corner from 25 yards.
"It's a sensational last-minute winner, a real bit of quality from young James," McInnes told BBC Scotland.
"We should be shouting from the rooftops with how good that is. It's different class."
Jonny Hayes shot the Dons in front right at the start of the second half but the Dons winger later conceded a penalty, converted by Rangers captained Andy Halliday.
Match-winner Maddison was introduced as a half-time substitute following a below par 45 minutes from the hosts.
"First half, I was really annoyed with how we played," said McInnes. "We were nowhere near like ourselves; we didn't commit to our passing, our tackling or our pressing. We stood off them and Rangers were enjoying the game too much.
"Second half, we put Jonny Hayes through the middle to give them something to think about and we score right away.
"Getting the goal gives the players that belief and confidence to go and get the win.
"They [Rangers] get a lifeline with the penalty kick, Jonny should do better with his positioning.
"We knew it would take a moment of quality to win it and for a young boy to produce that in the dying seconds with so much at stake tells you everything about him."
Aberdeen move up to second in the Premiership and McInnes, who has finished runners-up to Celtic in the past two seasons, thinks the victory can spur his team on.
"We deserved the three points," he added. "We scored two good goals and the game is about scoring goals.
"I can understand why Rangers might think they deserved something with all of their possession. But they never really cut us open and we were far more aggressive in the second half.
"We'll enjoy the day because for long spells it didn't look like we were going to get the win - but it's only three points.
"We recognise the strength of our opponents and I wouldn't be getting too distraught if we hadn't got the win.
"I know there are wins ahead of us and beating a team like Rangers can only help.
"We're here to try and do something at Aberdeen and hopefully the players sense that and we can go and be successful this season."
Manager Derek McInnes was full of praise for James Maddison's fabulous late goal as Aberdeen beat Rangers 2-1 at Pittodrie.