Strike duo Carlos Tevez and Emmanuel Adebayor scored the goals for the home side but it was deadline-day signing Johnson who caught the eye on his full debut.
The England Under-21 left winger, an £8m capture from Middlesbrough, won the penalty from which Tevez put City ahead in the 31st minute.
Bolton might have had a spot-kick of their own and Tevez hit the woodwork before Adebayor volleyed a second in spectacular style.
Victory moved City level on points with fourth-placed Liverpool and Mancini said of
Johnson: “That is why we bought him. He is a young player who wants to do well. He can play on the left and right and can also play behind the main striker. He can continue to grow and I think he can be a very important player for this club.”
Mancini also brushed aside fears that 33-year-old former Arsenal captain Patrick Vieira, who set up Adebayor’s goal on his home debut since returning to England, will be used sparingly because of his age.
“I played until I was 36 and I was still playing well,” the Italian added. “I won the Scudetto [Italian league title] at that age, so I see no reason why Patrick can’t carry on as well.”
Tevez scored his 15th in 15 games when Paul Robinson was judged to have fouled Johnson and Bolton goalkeeper Jussi Jaaskelainen failed to hold his powerful strike.
Togo forward Adebayor crowned the win with an acrobatic effort on 73 minutes after taking Vieira’s raking pass on his chest.