A first-half brace from Ed Upson inspired the Somerset side to a first home win of the season - but it was Wolves goalkeeper Hennessey who stole the headlines and ended the visitors' run of seven matches without defeat.
The Wales international shot-stopper saved a first-half Cox penalty and pulled off a string of second-half saves.
He said: "I was surprised that was Yeovil's first home win because in the first 45 minutes their appetite was good, their attitude was good and we quite simply didn't turn up.
"Having said that, at 1-0 you can't afford to miss penalties and that was without doubt a big turning point.
"I think they deserved to be in front at half-time, and second half I thought Hennessey was excellent and deserved his man of the match.
"In the Championship the blue sky doesn't exist every weekend, there are dark clouds and there will be difficult days ahead with ups and downs, bumps and bruises.
"There is no easy game in this league and you have to respect every team. Your attitude has to be right - and ours wasn't in the first half. On another day things could have been different, but Hennessey was excellent."
- Sports & Recreation