The visitors had a man sent off in controversial circumstances at the Etihad Stadium, with Gareth McAuley given his marching orders by Neil Swarbrick after two minutes, despite Craig Dawson having committed the foul on Wilfried Bony.
The Ivorian went on to break the deadlock - opening his account for City - with Fernando and David Silva also netting, handing the hosts a fitting response to back-to-back defeats to Burnley and Barcelona.
"It was a comfortable win because we played with one player more for 89 minutes," Pellegrini told BBC Sport. "We defended well and we concentrated well not to allow them to score."
Speaking about the sending off, Pellegrini did not address the matter of mistaken identity, but the Chilean did offer praise for Bony.
He added: "Unfortunately for West Brom, the rule is clear. He was the last man but the game is different when you have to play with one less player. It was a clear red card.
"Wilfied Bony is new in the squad and arrived after playing in the Africa Cup of Nations and he felt that. Every day, he is settling better and he is doing very well."
The win moves City - who lost their previous league game to Burnley before being dumped out of the UEFA Champions League by Barcelona - to within three points of Chelsea, though the leaders have two games in hand.
