The 34-year-old fired home on 45 and 69 minutes to take his tally for the Magpies to 191 18 of them this season as the Greek league leaders were brutally dismissed.
Trailing 3-1 from the first leg, there was little chance of Dusan Bajevic's side, despite their pedigree, forcing their way back into the tie.
But the way in which the Magpies dismantled them for the second time in a week to claim their eighth successive victory the first time they have achieved that feat since September 1994 and their most comprehensive of the season at home was hugely impressive.
Kieron Dyer had opened the scoring after 18 minutes with a back-heeled effort, and after Shearer had grabbed his first, Lee Bowyer made it 3-0 nine minutes after the break as Newcastle claimed their eighth successive win.
They extended their aggregate lead after 18 minutes when Lee Bowyer headed into the penalty area and Kieron Dyer controlled before back-heeling past Nikopolidis. Dyer had a shout for a penalty turned down after 26 minutes following Vallas' untidy challenge.
Shearer got his reward on the stroke of half-time when Dyer squared for his captain to fire home to claim his 190th goal for the club.
Both sides returned unchanged after the break and the home side tore into the Greeks once again. Dyer was relishing his new role up front with Shearer, and Olympiakos struggled to make it out of their own half.
The third goal duly arrived after 54 minutes, Nikopolidis scooping Bowyer's header off the line but finding himself powerless to keep out the midfielder's follow-up. Kafes briefly threatened to reduce the deficit on the hour, but took the ball early and fired well wide.
Shearer got his second of the night after 70 minutes, running on to Jenas's pass to round Nikopolidis and fire into the roof of the net before Lee Bowyer also helped himself to his second of the night. NEWCASTLE: Given, Carr (Ramage 67), Taylor, Andrew O'Brien, Hughes, Jenas, Bowyer, Butt, Robert (N'Zogbia 58), Dyer (Milner 58), Shearer.
OLYMPIAKOS: Nikopolidis, Mavrogenidis, Vallas, Anatolakis, Pantos, Maric, Stoltidis (Taralidis 79), Kafes, Djordjevic (Okkas 60), Giovanni (Filipakos 67), Castillo.
Referee: Konrad Plautz (Austria).