The Greek side were joined in the quarter-finals by four-time former winners Maccabi Tel Aviv and Spaniards Caja Laboral Vitoria, who advanced at the expense of Italian outfit Montepaschi Siena after beating them 74-62.
CSKA Moscow, Real Madrid, Panathinaikos Athens, Anadolu Efes Istanbul and Barcelona had earlier secured their passage to the best-of-five ties with games to spare in the marathon second group stage of the competition, featuring two pools of eight.
The winners of the playoffs, which start on Tuesday with 2010 champions Barcelona at home to six-time winners Panathinaikos, will advance to the May 10-12 Final Four series at London's O2 Arena.
In the other quarter-final ties, CSKA are at home to Caja Laboral, Real Madrid entertain Maccabi and Olympiakos take on Anadolu Efes in the opening games on Wednesday.
Olympiakos, who stunned CSKA in last season's final in Istanbul, led by a point at the end of the third quarter before Papanikolau, who finished with a game-high 21 points, sunk a pair of long-range shots to open an unassailable 10-point lead in the closing stages.
"Making the playoffs was our goal this season and I am very happy that I helped my team win," Papanikolau told the competition's official website (www.euroleague.net).
Coach Georgios Bartzokas added: "We feel our efforts have been rewarded because this Olympiakos team can't be compared to last season's side and it took a lot of enthusiasm to reach the quarter-finals.
"Now we have to concentrate on the playoff series with Efes and we have to be focused because I don't think the home court advantage will be a telling factor here."
Maccabi came through despite a 74-71 loss at 2010 champions Barcelona, easily the best team in the top 16 with a 13-1 record and favourites to reach the showpiece event in London.
Caja rode their luck all season but having played in fits and starts throughout the two group stages of Europe's premier club competition, they produced one of their best performances thanks to a stellar display by Polish centre Maciej Lampe.
The towering 27-year old, who has averaged 14.4 points this season, buried 27 and collected nine rebounds as Caja dominated proceedings from start to finish and sent their fans into raptures at the end of a long road to the playoffs.
The Basque outfit appeared out of contention early in the season after winning only one of their opening seven games, but somehow squeezed into the top 16 with three wins on the trot.
They then won four in a row at the start of the second group stage but five successive defeats had derailed their campaign before they got back on track with a crucial win at Khimki in the previous round.
"You can imagine how happy the players are as many of them are very young and this is the first time they have the opportunity of celebrating an achievement like this," Caja coach Zan Tabak said.
"It was a great night end especially so because we felt great support from our fans," added Tabak, who took over after Caja lost five of their opening six games and started his tenure with an 82-45 drubbing at Lithuanian champions Zalgiris Kaunas.
Elsewhere, CSKA Moscow secured top spot in their pool with a 69-63 win at Panathinaikos and Real Madrid enjoyed an 86-66 home rout of Efes on the back of 16 points from playmaker Sergio Lull and 15 by former Portland shooting guard Rudy Fernandez.
Istanbul rivals Fenerbahce and Besiktas meet later on Friday in the concluding top 16 match but only local pride will be at stake as both teams are out of contention to reach the playoffs.