Essex lost three wickets in the first 18 overs to raise home hopes of a first Championship win in 18 months.
But opener Nick Browne played a marathon defensive innings of 71 to prevent a shock result as Glamorgan shook hands at 17:45 BST.
Earlier, Will Bragg recorded a career-best 161 not out as Glamorgan declared their second innings on 386-8.
However, the hosts struggled to accelerate before the declaration.
The result means Essex lead Kent by seven points at the top of Division Two, while Glamorgan remain bottom despite a much-improved performance in the final two days of the match.
Glamorgan head coach Robert Croft told BBC Wales Sport:
"I thought our performance in the four days was far better than we've shown this season and it needed to be.
"It was a tough, hard-fought game, the type of cricket you probably see in division one as we decided to bat the opposition out of the game and give them no chance of winning.
"We backed ourselves to try to get the wickets, unfortunately we didn't quite get there but we've come out of this game with far more confidence..
"I think Will (Bragg) has been brilliant, he's scored two centuries and three fifties in six games and this has been his finest knock for Glamorgan, in a challenging situation."
Division Two leaders Essex drew with Glamorgan after being set an unlikely victory target of 334 in 70 overs.