Chelsea coach Frank Lampard named the youngest ever starting XI in Chelsea's Premier League history -- with an average age of 24 years and 88 days -- and the youngest of any team in the competition this season, and in the first half it was the hosts who went closest to scoring as a Willian free kick whistled past Vincente Guaita's post on 14 minutes.
In added time the Brazil international again nearly gave Chelsea the lead, but his close-range rebound of a Guaita parry was blocked impressively by former teammate Gary Cahill.
Meanwhile, Palace -- whose manager Roy Hodgson was coaching his 300th Premier League game -- failed to manage a single shot in the first half.
Chelsea soon broke the deadlock after the break as Willian flicked a ball through to Abraham in the Palace box for the England international to slot a finish past Guaita.
Pulisic, who has now scored five goals in Chelsea's last three Premier League games, wrapped up the victory with his 79th-minute strike, heading in after substitute Michy Batshuayi's blocked shot bounced up for the United States international.
The win was Chelsea's sixth in a row in the Premier League and marked their third clean sheet of the season. The result saw the Blues close the gap to Liverpool to five points as they overtook Manchester City, who play Liverpool on Sunday, and Leicester, who take on Arsenal later on Saturday.
"This is where we want to be," Pulisic told ESPN Brasil when asked about his side's league position after the game. "We've put in a lot of good performances, away from home and again today at home. It's not a big shock to me. We all believe in our style of play and we're enjoying it, so I think it's not a surprise."
Pulisic's impressive form has mirrored Chelsea's, but the 21-year-old said he could not take his performances for granted.
"Obviously I'm getting some time and I'm in form a bit, I'm getting some goals. Things are coming to me easy, but it's not always like that," he said.
"There's ups and downs in football, so I just have to keep going, keep improving. I want to be out there and continue to help my team. Coming here, it wasn't going to be easy right from the start, so it was just about staying positive and continuing to learn and improve."
Pulisic was substituted shortly after scoring and put it down in part to pain in his hip.
"I had some issues with my hip before and now in the game I started to feel it a bit ... but hopefully I'm going to get it checked out and it's going to be OK."