Albion are now on the road for the next two games, with trips to Derby County on Boxing Day followed by Sheffield United next Sunday and then a home date with Preston North End on New Year's Day.
City face successive home games - against Luton Town on Boxing Day, then Portsmouth on the Sunday, before a New Year's Day all West Country lunchtime clash with Plymouth Argyle at Home Park.
West Bromwich Albion boss Carlos Corberan told BBC Sport:
"We did not find the right fluidity in the first half.
"But we scored two good goals and won the game then.
"It was important for Mikey Johnston to score. It was good for him and the team. It will help him to keep growing as a player.
"When you know that you are scoring goals the previous year, you have a responsibility. You should be free to go again with this feeling."
Bristol City boss Liam Manning told BBC Sport:
"They were better than us in all areas. And we let in two soft goals.
"But all of us collectively have to be better. And I look at myself in that. Did I get it right?
"They're very well organised but we lacked energy and aggression and didn't have the quality to break them down.
"And we need to respond on Boxing Day. We can't afford to drift. We need wins."