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.
Foden slipped De Bruyne in on the right and Romain Saiss' foolish lunge brought the midfielder down just inside the box.
The Belgium international buried the penalty and Guardiola's unrelenting side continued to pile the pressure on.
City threatened to slice through Wolves several times before they did again to double their lead after 32 minutes.
De Bruyne had conducted City and he was at the heart of a slick move involving Ake, Rodrigo, Fernandinho and Foden.
De Bruyne then slipped in Raheem Sterling to cross for the arriving Foden to finish as Wolves were torn apart.
Wolves hit back from 2-0 down at Molineux last season to win 3-2 but without the backing of a vociferous fan-base – and the fact City were just too good – there was no way back.
Jimenez headed Adama Traore's cross wide five minutes before the break but it was Wolves' only opening of a chastening half.
It would have been worse had Patricio not turned De Bruyne's shot over after he was sent clear by Jesus' header.
There was no desire from City to sit on their lead after the break, demonstrated by their fierce pressing and Jesus' shot at Patricio.
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.