Ben Brereton Diaz left the hosts dumbfounded with a 20-second opener, only for the Eagles' two glittering gems single-handedly put the Blades to the sword - Olise set up Eze twice before notching a stunning strike for himself.
James McAtee had briefly restored the visitors' advantage in between Eze's strikes in an unmissable first half, but Roy Hodgson's men would still emerge victorious to make it back-to-back home wins in the Premier League, strengthening their survival bid while deepening Sheffield United's demotion woes.
An attacking reshuffle for the hosts saw both Olise and Jordan Ayew return to the XI following injury and the Africa Cup of Nations respectively, and the pair would endeavour to breach the goal of Ivo Grbic, making his Premier League debut for Chris Wilder's side.
Any pre-game Palace optimism stemming from Olise and Ayew's returns were dashed with only 20 seconds on the clock, though, as Gustavo Hamer fired a crisp cross-field pass to Brereton Diaz on the left, and the Chile attacker was given the freedom of the field to drift centrally and pick out the bottom corner with an exquisite curler.
The bewildered Eagles responded well to that immediate setback, though, and Sheffield United's advantage was wiped out on the 17-minute mark, as Eze ghosted past the Blades centre-backs to hook Olise's inswinging cross into the net with an acrobatic flick of the boot.
However, as was the case 20 seconds after kickoff, Selhurst Park was shocked into silence just three minutes after Eze's leveller, as Oli McBurnie demonstrated exemplary strength to hold the ball up and release McAtee, whose shot from the right-hand side of the box looped over a stranded Dean Henderson to give Sheffield United the lead again.
The boot of Marc Guehi helped McAtee's strike on its way into the roof of the goal - not that the visitors cared - but once again, Crystal Palace came up with an instant reply thanks to the Olise-Eze combination working its wonders again.
Rather than send another dangerous delivery into the box, Olise laid off Eze on the edge of the area, and the Englishman shifted the ball onto his left foot with a clever dummy before whipping a sumptuous 20-yard curler into the top corner.
After playing provider for Eze twice, Olise was nearly the beneficiary of his teammate's playmaking prowess from a 31st-minute free kick, and only a Vinicius Souza goal-line clearance prevented Hodgson's side from taking the lead for the first time in the match.
Wilder reverted to a more conservative setup with a couple of half-time alterations, but the Blades boss was then forced into an unwanted switch in the 51st minute, as a head injury for Grbic cut his Premier League debut short, much to his annoyance as Wes Foderingham stripped down.
The 33-year-old had only been on the pitch for 15 minutes before picking the ball out of his own net, though, as Jean-Philippe Mateta's attempted cross deflected back out to Olise on the edge of the D, and the Frenchman's first touch saw him rifle a glorious strike in off the post to put Palace ahead for the first time.
After running Sheffield United ragged for over an hour, both Olise and Eze were taken off as a precautionary measure due to knocks, potentially evoking some trepidation within the home crowd, which would not have been helped by Anel Ahmedhodzic heading against the crossbar in the 84th minute.
The basement side were gifted a minimum of 11 minutes of added time to try to steal a point, but Wilder's men were toothless when it mattered most, as the hosts came up trumps in the first-ever Premier League fixture between Palace and Sheffield United in which both teams have scored.
The Eagles' success temporarily takes them above Brentford into 14th place in the table, six points clear of the relegation zone, where Sheffield United continue to languish in 20th spot and are now nine points adrift of safety.
A so-called M23 derby with Brighton & Hove Albion at the Amex is next on Palace's agenda for Saturday, a couple of hours before Sheffield United welcome Aston Villa to Bramall Lane.