The teenage winger caused trouble for the Reds along the right flank throughout the 90 minutes.
He regularly took on the Liverpool full-backs, created a few promising chances of his own and for others and forced Alisson into action more than once.
After a first-half in which play swung between the teams - Liverpool scoring in each of their spells on top - Palace returned with a point to prove.
They began the second-half with remarkable speed and kept Liverpool under pressure for much of the next 45 minutes.
Impressive link-up play between Jean-Philippe Mateta and Odsonne Edouard allowed the latter to score and tee-up hopes of a fightback, however it wasn't to be for the south Londoners.
Olise and Palace were ultimately denied a comeback point as they pursued the equalising second by a late penalty decision which allowed Liverpool to bury the game.
The spirited performance merited credit for players across the team, and Olise scooped the Man of the Match award with 55.3% of the vote, beating Jeffrey Schlupp (16.2%) and Mateta (8.9%) to first place.