City were unplayable at times before losing their way after the break and Wolves made it nervy when Raul Jimenez pulled a goal back before Jesus struck in stoppage time.
Guardiola's men still sent out a message to champions Liverpool as they look to reclaim the title they surrendered last season.
De Bruyne, last term's Professional Footballers' Association player of the year, delivered a near faultless display while debutant Nathan Ake was assured.
City finished last season – just over a month ago – in disarray after their Champions League quarter-final exit to Lyon but immediately ended any fears of a hangover with a dominant first-half display.
City pinned them back and Wolves needed Rui Patricio to parry De Bruyne's free-kick but the dominant visitors kept probing and got their reward after 20 minutes.
But Wolves finally found their spark and created a flurry of chances, starting when Daniel Podence curled wide.
Ruben Neves' low drive was then cleared by Kyle Walker in a warning to City and Podence went closer after 59 minutes.
The forward was sent through by Neves only to chip over and, a minute later, Jimenez side-footed Traore's cross wide from six yards.
The striker did pull a goal back with 12 minutes left when Podence nutmegged De Bruyne and crossed for him to head in.
But Jesus ended any City fears when he made it 3-1 in injury time, his shot deflecting in off Conor Coady.