Mauricio Pochettino’s side entered the match off the back of successive away league defeats to Manchester United and Everton, but they managed to bounce back on home soil, netting twice in the early stages of the second period to secure all three points.
The result has moved the Blues into 10th position in the table, while Sheffield United remain rooted to the bottom, with the Blades on just eight points from their 17 league games this term.
Chelsea, as expected, dominated the possession in the early exchanges, with the Blues having almost 80% of the ball inside the opening 14 minutes, but Sheffield United were proving difficult to break down.
Conor Gallagher had a half-chance in the 15th minute after breaking past a couple of challenges, but his effort from distance never threatened to cause Sheffield United goalkeeper Wes Foderingham too much of an issue.
Mykhaylo Mudryk was next to try his luck in the 22nd minute, with the attacker striking over the crossbar after driving into a dangerous position.
Sheffield United had an opportunity of their own in the 24th minute, with Cameron Archer working space in a dangerous area before striking towards goal, but his effort was just too high.
Chelsea continued to dominate the ball as the first period approached its latter stages, but Sheffield United’s shape was excellent, with the Blues struggling to carve out clear opportunities.
Jackson charged through on the Sheffield United goal in the 38th minute, but excellent work from Foderingham meant more frustration for the home supporters.
There was another half-chance before the end of the first period, with Jackson working space in a dangerous area, but the striker’s effort was always moving wide of the post, and the two teams entered the break at 0-0.
Palmer had a shot deflected into the arms of the Sheffield United goalkeeper early in the second period, and it appeared that it could be one of those matches for the Blues.
However, Pochettino’s side managed to make the breakthrough in the 54th minute through Palmer, who turned a low cross from Raheem Sterling into the back of the net to spark jubilant scenes inside the stadium.
Chelsea then doubled their advantage in the 61st minute, with Palmer turning provider for Jackson, who managed to slot home at the far post, leaving Sheffield United with a mountain to climb.
Foderingham made a smart save to deny Sterling in the 68th minute, before Dorde Petrovic, who was in goal for Chelsea due to Robert Sanchez’s injury, did well to deny Gustavo Hamer from a free kick down the other end.
The hosts had two more opportunities late on, with Armando Broja somehow turning over the crossbar in the 84th minute after smart work from Palmer, who then saw a curling free kick kept out by Foderingham.
Christopher Nkunku was ultimately an unused substitute, but his return to the bench following a serious knee injury was a huge positive for Chelsea, who will welcome Newcastle United to Stamford Bridge in the quarter-finals of the EFL Cup on Tuesday night.
Sheffield United, meanwhile, will be aiming to bounce back from their latest defeat when they head to Aston Villa in the Premier League on December 22.
