Yaya Toure scored two penalties and then completed his hat-trick with a sublime third as City climbed to third in the Premier League, six points adrift of Chelsea but with three games in hand.
Fernandinho and Martin Demichelis were also on target as the bottom side capitulated after the dismissal of Fernando Amorebieta early in the second half.
The goals scored were a fine response to Chelsea and Liverpool - who both scored six goals on the same day - but Pellegrini was just as pleased not to concede.
The Chilean said: "It was a complete performance because we kept a clean sheet again. For me that is important.
"In the last part of the season I think we must be a very balanced team - not only scoring five goals but it is important not to concede goals.
"We scored five goals and we had a lot more chances.
"It is true that with only 10 players it was more difficult for Fulham, but before the player was sent off we scored two goals and had two or three more clear chances."
Toure's first two goals were penalties, both conceded by Amorebieta, the second of which brought about his dismissal, and his third took his tally for the season to 20.
The Ivory Coast midfielder is the third City player to reach that landmark this season after Sergio Aguero and Alvaro Negredo while Edin Dzeko, who missed the game through illness, has 18.
Pellegrini said: "I think it is important for Yaya, the way he plays.
"Maybe at the beginning of the season he received some criticism that he was not defending well, but defending is not allowing him to play freer.
"He is a very important player playing the way he likes to play. Scoring 20 goals for a midfielder is not easy in a season."
The victory puts City in good heart for their derby against Manchester United on Tuesday and another difficult trip to Arsenal next weekend.
Pellegrini said: "Always winning is good preparation for the next match.
"Winning today the way we did, scoring five goals and not conceding, it is always important but the derby is a special match, so we must try to forget about what we did today and start thinking about what we must do against Manchester United."