Manchester United modified their attacking approach at half-time amid concern they were clinging onto a 1-0 lead against City.
Anthony Martial earned a penalty with just 35 seconds on the clock at The Etihad which was converted by Bruno Fernandes, but United weathered a sustained spell of City dominance and were unconvincing on the counter-attack.
Martial spurned a gilt-edged chance to make it 3-0 but United were more incisive with their breakaways as they threatened to inflict a heavier defeat on City, eventually running out 2-0 winners.
“Every game lives its own life this season, it’s unpredictable, it can go up and down, that’s just human nature,” United manager Ole Gunnar Solskjaer said. “Today, we started really brightly on the front foot.
“When you get the 1-0 lead it sets a tone for the game. I thought we were excellent in the first 10 or 15 minutes, then settled into our shape, because we played too much on the result, and we adjusted that at half time to be more positive again and the second goal was incredible.
“We’ve got to do everything we can to keep the performance levels up, of course.”
City are still 11 points ahead of United with 10 games left and United threw away an eight-point advantage with six games remaining in 2012 when City won the title on goal difference.
United’s run of two wins from eight in the league prior to the derby victory could ultimately deny them a championship challenge and their 2-0 triumph was viewed by many as a possible marker for next season.
“None of these boys can look beyond Thursday,” Solskjaer stressed. “All we can think about is Thursday [against AC Milan]. One game at a time and see where we are at.
“We want to improve, I want the players to improve, we want to learn from this experience, we want to learn from Wednesday’s experience against Palace. We need to improve on so many things to get our consistency better.
“They’re 11 points ahead with 10 games to go, we need to be a better and focus on ourselves and be a better Man United. I think we’re a better Man United than we were 12, 13, 16 months ago.”