Guehi headed in the winner off a corner in the 87th minute on Sunday (Monday morning AEDT) to put Palace in the Champions League spots.
Palace overtook Everton and Chelsea and are four points behind third-placed Aston Villa.
The visitors opened the scoring with Eddie Nketiah's goal in the 20th minute, before Harry Wilson equalised for Fulham in the 38th.
It was the second league win in a row for Palace and the second straight defeat for Fulham, who stayed in 15th place.
Fulham had a goal disallowed in the second half after a video review.
The Premier League title race had been blown open on Saturday after Aston Villa struck in stoppage time to beat Arsenal 2-1, cutting the Gunners' lead to just two points after second-placed Manchester City beat Sunderland 3-0.
Liverpool's troubled title defence stumbled again when they dropped more points in a 3-3 draw at Leeds.
Georginio Rutter scored his first goal of the Premier League season in stoppage time to help Brighton salvage a 1-1 home draw against West Ham on Sunday.
Rutter found a gap between West Ham defenders to grab the equaliser with a shot from close range one minute into second-half added time. The goal was confirmed following a video review for a possible handball by the player in the build-up.
"He deserved it and we are quite happy that he is now on the sheet, which will give him a boost for the next game," Brighton coach Fabian Hurzeler said.
"Overall, it was a disappointing result. We wanted more but didn't deserve more, especially after the first-half performance."
Jarrod Bowen had put the visitors ahead with an angled shot in the 73rd minute.
It was the second straight league match without a win for Brighton, who are in seventh place.
West Ham, winless in their past four league games, stayed 18th and inside the relegation zone.
22°C