Begovic, 21, on loan from Portsmouth, pulled off a series of fine saves at The Galpharm to earn his side a point. The Canadian Under-20 international made 10 saves - three of them outstanding - to leave Ternent with just three wins from 14 league games.
Begovic tipped over from Gary Roberts before making a breathtaking one-handed stop from Andy Butler's bullet header.
Roberts' breakaway from his own half looked like ending in a goal, but 6ft 5in Begovic got down well to block. Huddersfield striker Liam Dickinson hit the outside of a post with a free-kick on the stroke of half-time.
Yeovil had little ambition, and it was only after the second-half introduction of substitutes Paul Warne and Gavin Tomlin that they tested the Huddersfield defence.
Begovic saved from Jon Worthington, Keigan Parker and Ian Craney after the break, but the goal would not come. There were boos for Ternent on the final whistle.