City's free-scoring ways have been well documented this term and a goal in each half from Edin Dzeko made the striker the fourth player in their ranks to reach 20 goals in all competitions.
Yaya Toure lashed home a 90th-minute drive to complete a memorable night for the blue half of Manchester and register his 21st strike of a remarkable individual campaign.
But Pellegrini made sure the efforts of his defence, who have now strung together five consecutive league clean sheets, did not go unnoticed.
United struggled against a defence superbly marshalled by talismanic captain Vincent Kompany and the often-maligned Martin Demichelis.
"I am very delighted because I think that we played very well, not only in attacking but also in defending," he said.
"We were a very compact and aggressive team from the beginning.
"I think that we are playing very well. Not only because we are scoring goals - in the last two games we scored eight goals - but also we have improved a lot in defending.
"This is our fifth clean sheet in a row and at the end of the season it is very important to try not to concede goals.
"That is why I am so happy about our performance today because against a very good team with important players we really didn't give any chances to score."
City are now three points behind Chelsea with home matches against Sunderland and Aston Villa in hand on the league leaders.
Pellegrini was aware of the lasting impact closing the gap with such a comprehensive win over the reigning champions might have on City's bid to bring the Premier League trophy back across town.
"It was a good performance - I don't know if it was the best performance because we have played a lot of good games," he said.
"It was important to do it today, here at Old Trafford, because it was one of the games in hand and the only one that we have to play away. So it was important to have three points more."
