Pep Guardiola's side are one point clear of second-placed Liverpool after Foden's fifth-minute header exacted a measure of revenge for City's Champions League quarter-final exit against Tottenham on Wednesday, a result that ended their bid to win an unprecedented quadruple.
"We could have lost the Premier League today - after Wednesday it was really tough. As a footballer, I could not have done what my players have done today," said Guardiola.
Liverpool can regain pole position if they win at struggling Cardiff on Sunday, but City have won their last 10 league matches to keep the destiny of the title in their own hands because the champions will hold a game in hand on Jurgen Klopp's men.
"It was very important for the race for the Premier League. We know we cannot drop points. It was tight, Tottenham had more chances than the previous two games," added Guardiola.
"We have been playing for the Premier League every three days for 10 months, you can feel the pressure.
"The title is still in our hands. We are fighting until the end."
As well as Foden's crucial contribution in only his second Premier League start, Guardiola was indebted to City goalkeeper Ederson for a series of fine saves as the champions gave a nervous display at the Etihad Stadium.
The only frustration for Guardiola was an injury to Belgium midfielder Kevin De Bruyne, who limped off again just before the break.
De Bruyne, only recently back from a knee problem, is unlikely to play in the midweek derby at Manchester United.
"We will see tomorrow but I think the next game he will be out," Guardiola said.
At Molineux, fourth-bottom Brighton moved three points clear of Cardiff after a gritty stalemate against Wolves.
Chris Hughton's men, who have a game in hand on Cardiff, needed a man-of-the-match display from Australian goalkeeper Mat Ryan to avoid a fifth successive defeat.
Ayoze Perez's hat-trick effectively sealed Newcastle's safety as the Magpies beat struggling Southampton 3-1.
Perez struck in the 27th and 31st minutes at St James' Park before Mario Lemina reduced the deficit in the 58th minute.
Perez completed his treble with four minutes left to move Newcastle 10 points clear of the bottom three, while Southampton are five points above the drop zone.
Gerard Deulofeu's brace lifted Watford to seventh place with a 2-1 victory at relegated Huddersfield.
Deulofeu, the hero of Watford's FA Cup semi-final win over Wolves, put the Hornets ahead with a deft dink into the top corner in the fifth minute at the John Smith's Stadium.
The Spanish winger netted again in the 80th minute after Jonas Lossl saved Abdoulaye Doucoure's effort.
Huddersfield's stoppage-time reply from Karlan Grant couldn't stop the Terriers suffering a 14th home defeat this term.
Watford's rise up the table was aided by Leicester's 2-2 draw at West Ham, which dropped Brendan Rodgers' team to eighth place.
Michail Antonio put West Ham ahead in the 38th minute with a powerful header from Mark Noble's cross.
Jamie Vardy equalised in the 67th minute with a cool finish from Ben Chilwell's cross for his 16th goal of the season.
Lucas Perez restored West Ham's lead with an 82nd-minute tap-in just four minutes after coming on.
But, after Perez had a second goal wrongly ruled out for offside, Harvey Barnes rescued Rodgers' side with an equaliser two minutes into stoppage-time.
Relegated Fulham finally earned their first Premier League away win this season with a 1-0 success at Bournemouth.
The Cottagers took the points in the 53rd minute when Serbian striker Aleksandar Mitrovic was clattered in the penalty area by Jack Simpson and stepped up to convert the spot-kick himself.