Man City made the breakthrough in the 35th minute of the contest, and it was a brilliant goal from Gvardiol, who collected a pass from Jack Grealish before finding the bottom corner of the net.
Newcastle came close to levelling the scores late in the first period through Joelinton, but Man City goalkeeper Ederson was on hand to make a brilliant point-blank save to deny his fellow Brazilian.
The Magpies will have been relatively pleased with their work in the opening 45 minutes of action, but the Citizens entered the half-time interval with a narrow lead courtesy of Gvardiol's clever finish.
Newcastle were awarded a penalty in the 56th minute of the contest when Gordon went down under a challenge from Ederson, with the goalkeeper also picking up a yellow card.
Gordon stepped up and sent Ederson the wrong way to level the scores at St James' Park, and the momentum was suddenly with Newcastle, as they searched for a second goal.
Sean Longstaff missed a late opportunity for Newcastle, sending one just wide, but Man City were struggling for a cutting edge in the final third during a quiet afternoon for Erling Haaland.
The result has moved Newcastle up into fifth position in the Premier League table, boasting 11 points from six matches, while Man City have moved two points clear of second-placed Liverpool at the summit.
NEWCASTLE VS. MAN CITY HIGHLIGHTS
Josko Gvardiol goal vs. Newcastle (35th min, Newcastle 0-1 Man City)
The breakthrough arrives in the 35th minute of the contest at St James' Park, and it is a goal for the left-back Gvardiol, who brilliantly picks out the corner after being found by Grealish.
The Croatian has now found the back of the net on six occasions for the Citizens since his arrival, and it is a blow for Newcastle, who will have been pleased with their work in the opening 35 minutes.
Anthony Gordon goal vs. Man City (58th min, Newcastle 1-1 Man City)
Gordon, having been fouled by Ederson inside the box, steps forward to level the scores from the penalty spot.
It is a brilliant penalty from the Englishman, who sends Ederson the wrong way, sparking jubilant scenes inside the stadium. All square with little over 30 minutes of football to play at St James' Park.
MAN OF THE MATCH - JOSKO GVARDIOL
Gvardiol was the best player on the pitch at St James' Park, with the Man City defender once again showing his class at both ends of the field.
The Croatian demonstrated wonderful composure to send the visitors ahead, while he made two tackles and finished with a pass success rate of 85% during a strong performance.
There were a number of talented attackers on the field on Saturday, but Gvardiol put in a man-of-the-match display for the reigning Premier League champions.
NEWCASTLE VS. MAN CITY MATCH STATS
Possession: Newcastle 35%-65% Man City
Shots: Newcastle 10-16 Man City
Shots on target: Newcastle 4-6 Man City
Corners: Newcastle 5-6 Man City
Fouls: Newcastle 14-10 Man City
BEST STAT
WHAT NEXT?
Man City will now switch their attention to the Champions League, and they will be looking for their first win in the competition this season when they head to Slovan Bratislava on Tuesday night; the Citizens will then return to Premier League action at home to Fulham next weekend.
Newcastle, meanwhile, will take on League Two outfit AFC Wimbledon in the EFL Cup on Tuesday evening, before facing Everton in the Premier League next weekend.