The Ivory Coast international twice converted coolly from the penalty spot following fouls by Fernando Amorebieta - the second of which, on David Silva, saw the centre-back sent off.
Toure then added a spectacular third with a 30-yard effort similar to his game-changing strike in this month's Capital One Cup final victory over Sunderland, before Fernandinho and Martin Demichelis also found the net to ensure the Premier League's bottom club were well beaten and City kept pace with Chelsea and Liverpool in the title race.
Seen largely as a holding midfielder when he moved to Manchester from Barcelona in 2010, Toure was converted into a powerful attacking force under Roberto Mancini.
He has arguably scaled new heights under the Italian's successor and Pellegrini believes the high-profile criticism Toure has received from some pundits, due to his perceived tendency to shirk defensive duties, somewhat misses the point.
"I think it is important for Yaya, the way he plays," Pellegrini said.
"Maybe at the beginning of the season he received some criticism about not defending well but, for me, it is very easy to tell Yaya to stay back and defend.
"Then you are not allowing him to play free. I think 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."
Title rivals Chelsea and Liverpool put six goals apiece past Arsenal and Cardiff City respectively on Saturday, meaning City's return to the free-scoring form they exhibited earlier in the campaign was most welcome ahead of away trips to Manchester United and Arsenal.
However, Pellegrini was also keen to praise his defensive unit, who recorded a fourth consecutive Premier League clean sheet for the first time since January 2013.
"It was a complete performance because we kept a clean sheet again and that, for me, is important," he added.
"In the last part of the season, I think we must be a very balanced team - not only scoring goals but it is important not to concede easy goals. We scored five goals, we had a lot more chances.
"It is true also that with 10 players it was more difficult for Fulham. But before the player was sent off we had two or three clear chances."
