Obika's late goal was Millwall's first attempt on target in a game which saw Yeovil defend heroically throughout.
The Glovers went ahead with their first shot after 26 minutes, Gavin Williams setting up Dean Bowditch for a crisp finish from 10 yards.
Williams almost added another three minutes later and he and Shaun MacDonald both went close in the second half.
But just when Yeovil looked certain to claim three points, Obika - who started the season on loan with the Somerset side - was in the right place to loop a header over home goalkeeper Alex McCarthy.
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