Jaydev (217), who has scores of 193, 64 and 0 so far this season, put on 174 for the sixth wicket with Chirag Jani (100 not out), before Saurashtra declared their first essay.
Chesteshwar Pujara also made a patient 93 off 246 deliveries.
It was struggle once again for the Maharashtra's bowlers, who nearly conceded a lead despite scoring 600-plus against Delhi last week.
In reply, Maharashtra were 18 for no loss in six overs.
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Openers Swapnil Gugale (10 batting) and Murtaza Trunkwala (7) were holding the fort for Maharashtra at stumps on the second day of the four-day match.
Brief Scores:
Saurashtra: 657 for eight decl in 170.5 overs (Jaydev Shah 217, Sheldon Jackson 105, Chirag Jani 100 not out, Cheteshwar Pujara 93; Mohsin Sayyed 4/90).
Maharashtra: 18 for no loss in six overs (Swapnil Gugale 10 not out, Murtuza Trunkwala 7 not out).