City, who made six changes ahead of this weekend's FA Cup final against Chelsea, moved to within two points of league leaders Arsenal with two matches remaining.
Despite dominating possession at the Etihad Stadium, Guardiola's side initially struggled to create clear chances. Palace threatened early when Jean-Philippe Mateta thought he had forced the ball over the line, but the move was eventually ruled out for offside.
City gradually took control and finally broke through after 33 minutes. Foden produced a clever backheel in a crowded area to release Antoine Semenyo, who calmly beat Dean Henderson to open the scoring.
The England midfielder was again at the centre of City's second goal before half-time. Foden picked out Omar Marmoush with another precise pass, and the forward finished confidently to give the hosts complete control before the break.
Palace manager Oliver Glasner introduced several attacking substitutions after half-time, including Ismaïla Sarr and Adam Wharton, but City remained comfortable throughout. Substitute Rayan Cherki then supplied a fine assist for Savinho, who wrapped up the victory six minutes from time.
Guardiola reserved special praise for Foden after the match, highlighting the midfielder's creativity and ability to unlock games in tight spaces.
"You need the quality, the spark, the talent, the vision, something," Guardiola said. "It's not in the tactical boards, it's not in the meetings or videos. Phil receives the ball in small spaces and creates something special."
Foden admitted competition for places had been difficult at times this season but said patience had been important.
"I struggled to find my place in the team at one stage," Foden said. "When you have quality players around you, you have to stay patient and keep working hard. When your chance comes, you have to take it."
The midfielder also praised City's squad depth during the demanding run-in.
"It's massively important to have fresh players coming in at this stage of the season," he added. "We knew this was a must-win game."
City now turn their attention to the FA Cup final before returning to league action against AFC Bournemouth and Aston Villa in their final two matches.
Guardiola admitted the title race remains out of City's hands but insisted his players must stay focused.
"I cannot ask for more from the team," Guardiola said. "Now we focus on the last two league games and see what happens."