However, the visitors did not have a great start to their chase as they lost opener Amogh Desai before the close of play.
Starting the day at 222 for two, Jharkhand batsmen failed to capitalise on a good start as they lost wickets at regular intervals.
Saurabh Tiwary (35) was the first one to go, losing his wicket to a needless run out.
Ishank Jaggi failed to make a significant addition to his overnight total as he fell to Bandekar on 57.
Amir Hashmi and wicketkeeper-batsman Shiv Gautam tried to resurrect the hosts' innings, but with latter falling prey to Shadab Jakati in the 21st over of the day, things certainly did not look good for Jamshedpur.
With Hashmi following suit 35 runs later, Jamshedpur were reduced to 302 for six before Kumar Deobrat struck a well made half-century to take the hosts pass 350-run mark.
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Responding to Jamshedpur's first innings total, Goa did not have an auspicious beginning as Desai edged one to wicketkeeper Gautam off Shahbaz Nadeem.
At the draw of stumps, Swapnil Asnodkar was unbeaten at three and giving him company was Manvinder Bisla at three.
Brief Score:
Jamshedpur 1st innings: 360 for all out in 151.4 overs (Manish Vardhan 73, Kumar Deobrat 58; Saurabh Bandekar 76/4)
Goa 1st innings: 24 for one in 14 overs (Amogh Desai 13; Shahbaaz Nadeem 7/1).