Forward Diogo Jota was killed in a car accident alongside his brother Andre Silva.
Reds legend Ian Rush and Palace chairman Steve Parish laid wreaths on the side of the pitch before kickoff, while the Liverpool end was awash with banners and flags paying tribute to the Portuguese international.
A minute’s silence, however, had to be cut short because of disturbances in the crowd.
Jota’s death has dampened the excitement over Liverpool’s transfer spending spree to build on a squad that romped to a record-equalling 20th league title last season.
All four of their new signings – Ekitike, Florian Wirtz, Frimpong and Milos Kerkez – started the game.
Ekitike’s role this season could depend on whether Liverpool are successful in their pursuit of Newcastle striker Alexander Isak.
But the Frenchman – signed from Eintracht Frankfurt last month – did his case to be Slot’s preferred No 9 no harm at all.
Wirtz also bagged his first assist for the Reds when Ekitike spun on to the German’s pass and fired into the far corner after just four minutes.
Palace were making their first ever appearance in the fixture but the Eagles again showed their ability to match one of the Premier League’s giants over 90 minutes.
Mateta missed a glorious chance to level when he failed to beat Alisson Becker when one-on-one.
But from the rebound Sarr charged into the box and was tripped by an out-of-sorts Virgil van Dijk.
Mateta coolly sent Alisson the wrong way from the penalty spot to equalise.
Liverpool’s players were sporting a “Forever 20” emblem, referencing Jota’s now-retired shirt number, that they will wear all season.
The Liverpool fans had risen to chant Jota’s name as the game entered the 20th minute when their side retook the lead.
Frimpong’s chipped cross caught out Henderson and flew into the far corner.
Ekitike wasted a great chance for his second early in the second half from another Wirtz pass as this time he fired over.
However, Slot’s new-look side are still to find the right balance between attack and defence as has been evidenced during pre-season.
“The combinations look sometimes sharper now,” said Slot on the difference in his side to last season.
“We are able to create more but we are conceding at the moment more as well. If you want to compete to win the league, you cannot concede these chances.
“We conceded too much today to win the game.”
Palace were a constant threat with balls in behind the Reds’ defence and levelled again 13 minutes from time.
Sarr sped on to Adam Wharton’s through ball and calmly slotted past Alisson for his fourth goal in seven games against Liverpool and sent the game to a shootout without extra time.
Youngster Justin Devenny was the unlikely hero as he blasted the winning spot-kick high past Alisson, showing Salah, Mac Allister and Elliott how it is done.