On a busy day of top-flight action, the pitchside VAR monitor was used in the Premier League for the first time at Norwich and Arsenal were held to a 1-1 draw by Sheffield United.
It was the drama at the Etihad Stadium that took the spotlight as Fernandinho's last-gasp blunder left Guardiola in no mood to party after City's faint hopes of retaining the title suffered another hammer blow.
The champions trail Liverpool by 13 points ahead of the runaway leaders' clash with rivals Manchester United on Sunday.
Palace won the corresponding fixture at the Etihad Stadium last season and the south Londoners took a shock lead in the 39th minute.
Cenk Tosun marked his first league start since his loan move from Everton with his maiden goal for the Eagles, the Turkish striker netting a close-range strike from Martin Kelly's flick.
Sergio Aguero appeared to have turned the game on its head in the 82nd minute when the Argentine striker turned in Gabriel Jesus's cross for his 250th goal in 360 games for the club.
Aguero put City ahead in the 87th minute with a typically predatory header from Benjamin Mendy's cross.
But there was a sting in the tale for Guardiola as Fernandinho turned Wilfried Zaha's cross into his own net in the 90th minute to end second-placed City's run of three successive league wins.
At Vicarage Road, Troy Deeney's 70th-minute spot-kick was saved by Paulo Gazzaniga before Tottenham's Erik Lamela was denied a last-gasp winner by Ignacio Pussetto's goal-line clearance.
With England captain Harry Kane sidelined after hamstring surgery, Tottenham have gone three league games without scoring.