Sergio Aguero opened the scoring in the ninth minute, sweeping home his 17th goal of the season, as many as West Brom have managed from their entire squad.
Yaya Toure then produced a deft touch 15 minutes later to a low ball from Aleksandar Kolarov, and but for a fine save from Boaz Myhill to deny Aguero it could have been 3-0 before the interval.
A Toure penalty after 72 minutes gave City their third before Albion pulled one back courtesy of a Costel Pantilimon own goal four minutes from time and added a second four minutes into injury time from Victor Anichebe.
The scoreline was perhaps rough justice on City, who remain six points behind leaders Arsenal at the top of the Barclays Premier League, but it at least ended back-to-back away defeats.
"We played very well. In other (away) games we played as well as we did in this game, but for some reason we didn't score the two early goals like we did here," assessed Pellegrini.
"We had a lot of chances to score, and for 45 minutes we were very good. The scoreline doesn't tell the story. It was not such a close match as the score says.
"Maybe we were thinking of the next game before we finished this one, and in football the game is not over until the final whistle.
"So they scored two late goals, which is why it finished 3-2, but we certainly had more advantage over the whole game.
"The game was more easy than we thought which is why we relaxed in the final few minutes."
For Pellegrini, the result rather than the scoreline was all that mattered, adding: "We were not trying to send a message, we were trying to add points which is more important.
"For us it was important to win away, and we'll try to do it again on Saturday (at Southampton) before we then play Arsenal."
Source: Manchester City MAD