Sergio Aguero opened the scoring from the penalty spot after Chris Baird brought down Johnson before a Baird own goal and Edin Dzeko strike sealed the win for City.
The result means City go three points clear at the top of the table with second-placed Manchester United playing Chelsea tomorrow.
City have also now won 12 out of 12 games at home this season as they recovered from a 1-0 defeat in midweek at Everton.
"It was obviously important to bounce back and get a good result today [Saturday] after the Everton game where we didn't play as well as we should," Johnson told ESPN.
"It's nice to get in early and get the three points and put the pressure on the other teams.
"We're looking forward to seeing the results tomorrow, and as I say, putting them under pressure."
Goalscorer Dzeko believes City's early lead, after Aguero's 10th-minute penalty, helped them to take control of the match in tricky conditions.
"From the beginning it was a very hard pitch and when it's like this it's always better to score at the beginning of the game, then it's easier for us to play," Dzeko said.
The striker believes goal difference could also be crucial come the end of the season with matters very tight at the top of the table.
"Every goal is important so goal difference is very important. We now have three points more than United but they have a tough game tomorrow [Sunday].
"It was a good game to win today [Saturday]."
City manager Roberto Mancini was pleased with the performance and believes his side are back on track after their loss against Everton.
"The players were fantastic and played very well. It was not easy as Fulham are a good team," Mancini told ESPN.
"This is a very important result after one defeat. We need to fight against the top teams and we need to win.
"There are some difficult moments in the season and January for us was so-so. Hopefully now we can continue to win the next game."
Mancini also played down an injury to midfielder Samir Nasri.
"Samir Nasri had a small problem and in the next few days we can see how he is," Mancini said.