Wright-Phillips and Johnson both produced fine second-half finishes before substitute trialist Luca Scapuzzi added a third late on, as City recorded a laboured but overall satisfactory win in the Irish capital.
Gareth Barry captained City in the absence of the still holidaying and soon to be disposed of Carlos Tevez, while Wright-Phillips, Stefan Savic and Johnson were the more illustrious of his team-mates on show.
The Aviva Stadium is a beautiful addition to a fine capital city but much of the football on show in the first half lacked any real incision or cohesion; not surprising given this was a City side that had never previously played together.
Credit to the Airtricity XI though as they were well organised and more than a match for their Premier League counterparts, whose best chance of the first half saw Wright-Phillips test Ger Doherty with an angled drive.
Johnson fizzed one over after cutting onto his left foot but City were largely subdued by an Irish side rich in endeavour if lacking a cutting edge in the final third.
As Johnson grew disheartened with a lack of service he began to wander and almost profited when in a more central role he side-footed a yard wide from Vladimir Weiss' pullback.
Wright-Phillips has enjoyed a productive pre-season to date and so it continued just after the break when he scored a goal of genuine quality, out of keeping with much of what had preceded it.
Barry was the architect with a raking pass and after letting the ball drop over his shoulder Wright-Phillips did his best David Platt impersonation circa 1990 as he slammed a fine volley beyond Doherty.
As if awoken from his relative slumber by his fellow winger's moment of opportunism Johnson then reminded Mancini of his own qualities by doubling City's lead.
Again it was Barry who played the provider as his pass dissected Airtricity's backline to allow Johnson to register with a smart finish with the outside of his left foot.
The highly-rated James McClean showed the odd moment of promise as Airtricity rallied but Stuart Taylor in City's goal was never really tested.
City substitute Scapuzzi made it three five minutes from time when he converted Johnson's smart slide-rule pass.
City did what they had to do but rarely got out of second gear in a performance that is unlikely to give Sergio Aguero too many sleepless nights as he looks to start next week's Community Shield against Manchester United.