Palmer unlocked a determined visiting defence when he poked home the ball from six metres after a one-two with Raheem Sterling in the 54th minute.
Palmer then turned provider in the 61st when United goalkeeper Wes Foderingham could only parry the ball to the midfielder after a goalmouth melee and he fed Jackson who was unmarked at the far post to turn the ball home.
Sheffield United, under newly returned coach Chris Wilder, had managed to suffocate Chelsea in the first half.
Chelsea forwards Mykhailo Mudryk and Jackson made forays into the visitors’ area but were constantly frustrated by the disciplined defence with every man behind the ball.
Mauricio Pochettino’s expensively-assembled side produced only one shot on target in the half, a Conor Gallagher effort that was calmly collected by Foderingham.
Pochettino changed his formation and switched Sterling and Cole’s positions in the second half to try to break United’s stranglehold.
“In the first half we didn’t find a way to break the low block,” he said. “We changed to try to find a better solution … better positions.”
Wilder, who has been in charge of Sheffield for only 10 days in his second stint, earning a win against Brentford after a defeat by Liverpool, blamed Saturday’s loss on the inexperience of his side and Chelsea’s quality.
“They have players all over the pitch that are world class,” he said.
Chelsea’s third home league win of the season sent them up to 10th place, above London neighbours Fulham and Brentford. United remained rooted to the foot of the table.