Guardiola's side could not afford to slip up at Molineux if they wanted to keep pace with the champions and they raced into a two-goal lead before half-time thanks to Kevin De Bruyne's penalty and Foden's cool finish.
City's swaggering first half gave way to an anxious spell as Wolves dominated after the interval and they had to cling on after Raul Jimenez got one back before Gabriel Jesus sealed the points in stoppage time.
Foden's goal was a welcome morale boost in his first match since the midfielder was sent home in disgrace, along with Manchester United's Mason Greenwood, after the pair broke coronavirus protocols.
"For the goal and in the second half Foden played incredibly well, he helped us keep the ball," Guardiola said.
While City equalled Aston Villa's record of winning 10 consecutive opening fixtures to a top-flight season, there is little doubt Liverpool remain the Premier League's preeminent force for now.
But Guardiola was delighted to open with a victory given the shorter than usual pre-season.
"We could not run much because we are tired in our legs but in general we did a good game," he said.
Wolves v Man City player ratings
"The period that we are in, the situation that we had this last two weeks, I expected some moments where we suffer but in general we controlled it well.
"It was a good performance. We know how difficult it is in this stadium.
"Sometimes we need more time to get to our best condition but it was a good start to come here and win."
It feels like a crucial season for City and Guardiola as they look to regain the title they won in 2018 and 2019.
Guardiola says he needs to "deserve" an extension to his City contract rather than just be handed one as he enters the final year of his current deal.
After finishing 18 points behind Liverpool and suffering a shock Champions League quarter-final defeat against Lyon, City need to push the champions harder this term and the early signs were encouraging.