Goals from Pedro Rodriguez, Willian and Callum Hudson-Odoi earned Chelsea a 3-0 win over Dynamo Kiev at Stamford Bridge.
Chelsea won their second knockout match in a matter of days after a midweek penalty shoot-out victory over Tottenham Hotspur in the League Cup.
Arsenal defeated Ukraine's Vorskla Poltava 4-2 in the Europa League, while in-form Chelsea registered a 1-0 win away to PAOK in Greece.
Conte was dismissed just four weeks before the start of the season despite winning the Premier League in his debut campaign and the FA Cup last season.
Courtois' future at Stamford Bridge remains uncertain, but Sarri hopes the Belgium goalkeeper will stay.
The teams meet in Kazan on Friday evening with Brazil the favourites, despite the quality in a Belgian side captained by Hazard, who plays with Willian at Chelsea.
After successive defeats by Manchester City and Manchester United, injury-hit Palace proved to be the ideal opponents for Antonio Conte's side at Stamford Bridge.
Just four days before facing Barcelona in the first leg of their Champions League last 16 tie, Conte named a much-changed side with Thibaut Courtois, Cesar Azpilicueta, N'Golo Kante and Eden Hazard not even included in the Italian's squad.
Chelsea rested the likes of Eden Hazard and Cesc Fabregas for the Premier League match against Stoke City.
Looking to bounce back from the trauma of letting a 3-0 lead slip in their 3-3 draw at Sevilla in the Champions League, Liverpool went ahead in the 65th minute through former Chelsea man Mohamed Salah.
Willian scored twice and won a pair of penalties as Chelsea thrashed 10-man Qarabag 4-0 in Baku to guarantee Antonio Conte's side a top-two finish in Group C.
Dele Alli and Harry Kane kept Tottenham Hotspur in the Premier League title hunt as their side torpedoed Arsenal 2-0 while Chelsea maintained their advantage by winning 3-0 at Everton earlier in the day.
Nemanja Matic's thunderous long-range effort sealed a final date for Chelsea against Arsenal or Manchester City, who meet in the second FA Cup semi-final on Sunday.
Willian scored in the 83rd minute for Chelsea in the 2-1 win over Dynamo Kiev in Champions League
Chelsea F.C. manager Jose Mourinho saw his side hit the woodwork through the recalled Eden Hazard and Willian, but had to settle for a point.
Willian scored twice -- in the 37th second and again the 42nd minute -- as Brazil rebounded from a humbling loss to Chile last Thursday to beat Venezuela 3-1 in their 2018 World Cup qualifier.
Willian, Oscar, Diego Costa and Cesc Fabregas netted a goal as Chelsea F.C. started their Champions League campaign with a 4-0 win over Maccabi Tel Aviv.
Brazil have won eight consecutive matches since the arrival of coach Dunga after the humiliating loss at the 2014 World Cup in their own backyard. Willian added Brazil would go into the Copa America, staring on June 12, with a lot of confidence.