The Briton had just set his fastest time in the W04, a 1m19.519s, when he slid across the gravel and nosed into the tyres at Dry Sack.
He was unhurt in the crash, which Mercedes later diagnosed as caused by a rear brake problem.
Hamilton had completed 15 laps at the time - just four more than Nico Rosberg managed for the squad before he was forced to abandon his opening day programme due to an electrical issue.
Hamilton's crash caused one of three red flags, with Daniel Ricciardo's Toro Rosso stopping early on and Luiz Razia – confirmed as Marussia's second driver for 2013 - slowing to a halt on the main straight in the final minutes.
As he did so Grosjean, who was already fastest, set a new overall best at Jerez in the Lotus E21.
The Frenchman clocked a 1m18.828s, some three hundredths of a second faster than Jenson Button's day one benchmark in the McLaren.
Force India's Paul di Resta also found late gains, moving up into second position in the final minutes of the morning.
The Briton will hand control of the VJM06 to the team's simulator driver James Rossiter this afternoon.
Toro Rosso's Ricciardo beat compatriot Mark Webber's Red Bull to third, the pair separated by less than a quarter of a second.
On his second day for Sauber Nico Hulkenberg finished fifth fastest, fractions ahead of Hamilton in the stricken W04.
Sergio Perez was less than six hundredths of a second down the road from Hamilton – the man he replaced at McLaren – on what was his first day of testing the MP4-28.
Ferrari spent much of its morning on evaluative runs, with Felipe Massa eventually ending the second morning in eighth position, just over one second off Grosjean.
On his second day for Caterham, Giedo van der Garde fell one thousandth short of matching his best time Tuesday, but still did enough to edge out Marussia debutant Razia and Pastor Maldonado in the 2012-spec Williams FW34.
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- Nico Rosberg
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