Manchester United manager Sir Alex Ferguson admitted he changed his team to face Everton after City's loss to Southampton on Saturday.
The Red Devils moved 12 points clear at the top of the table with victory over the Toffees, courtesy of goals from Ryan Giggs and Robin van Persie.
Ferguson said it was a crucial win to give them even more of a buffer over their city rivals.
"I did (change my team after seeing Manchester City result). I thought that this is going to be a more important game today, because it can give us an important lead and we can make changes later," he told Sky Sports.
"We knew that if we could get a result today it puts us in a fantastic position.
"We got to win our games, it doesn't matter what happens to Manchester City, I've always said we have to concentrate on our own games and we'll be OK."
Veteran Giggs struck early on, to continue his record of having scored in every Premier League season.
Ferguson was full of praise for the Welshman.
"His legacy lives on, he's a fantastic human being, today again 39 years of age, he's up and down that pitch all day and showing fantastic energy. It's wonderful to see," he said.
"The first half, for 20 minutes I thought they dominated, a couple of near things, corners are always a threat, great delivery from Baines, and we saw that through.
"Second half we were much better without scoring the goals, we were really in control."
United now head to Madrid to take on Real in the Champions League on Wednesday and Ferguson is looking forward to the clash.
"I had a chat with Mourinho (before the game). He had a great result yesterday," he said.
"It should be a fantastic game on Wednesday, I just hope we can get the team out on the pitch that I want."
United's second goal, from Van Persie, came right at the end of the first half and Everton manager David Moyes admitted it was a bad time to lose another goal.
"We didn't start very well, United were very good in the opening period, the goal just before half-time made it very difficult for us, but credit to the lads, we stuck in but we're a bit disappointed not to get a goal," he said.
"They played as if they meant it today. They didn't play as if they were thinking about a midweek game, that's for sure. They tackled and competed, especially in the first half."
The Scot also feels the gap at the top may prove too much for reigning champions Manchester City to overhaul now.
"I think 12 points against a club like Manchester United is a big gap to make up," he added.
"Football doesn't always go the way it's meant to be but it looks a lot of points between the two teams now."