However, the visiting team lost a few wickets after that as Nottinghamshire closed in on their lower-order.
Vijay, who struggled to get going in the Test series against England, scored 56 off 95 balls.
Vijay's knock included nine boundaries.
Earlier, Nottinghamshire failed to capitalise on the toss after electing to bat as they were bowled out in 58.1 overs. For Essex, medium pacer Jamie Porter was the most successful bowler, returning figures of 4/50.
In another county match recently, India's left-arm spinner Axar Patel claimed nine wickets for Durham, including seven in an innings.
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