Dimitris Siovas and striker Rafik Djebbour set the home side on their way in the first half, before Giannis Maniatis and another Djebbour strike sealed the points for Leonardo Jardim's team who have won their opening two matches.
Siovas was first to the rebound after Jose Holebas's free kick cannoned off the Levadiakos defensive wall, side-footing home after just five minutes.
Algeria forward Djebbour then drove in a low diagonal shot seven minutes before half-time, after the visiting goalkeeper failed to deal with Paulo Machado's free-kick.
Greece midfielder Maniatis made it 3-0 three minutes after the hour mark, and Djebbour slid home Olympiakos' fourth, and his second, 15 minutes from full-time, after a nice lay-off from winger Djamel Abdoun.
The win, combined with Panathinaikos' low-key 1-1 home draw against PAS Giannina 24 hours earlier, saw Olympiakos put some early daylight between themselves and the Greens.
Elsewhere, there was disappointment for cash-strapped AEK Athens' revamped, youthful team after they went down to their second narrow defeat in succession.
Vangelis Vlachos' side lost 1-0 away against Skoda Xanthi, thanks to a 70th-minute goal from Marko Markovski, while Panionios continued their 100 percent start to the season, with Kostas Mendrinos' second-half strike ensuring a 1-0 victory at Veria.
Atromitos, eliminated from the Europa League by Newcastle United on Thursday, take on PAOK Thessaloniki on Monday in the highlight of the Round Two fixtures.