For the Hatters, it was their first away point of the season at the fifth attempt, while Yeovil, decimated by injuries, finished strongly enough to have won the game.
They now have to travel to Leeds on Saturday but manager, Russell Slade, is in a buoyant mood.
"Considering the injuries we have had and considering that our budget is much smaller than some of the teams we are up against, I think we are having a magnificent time," he said.
"Some fans are impatient but most of them know what we are trying to do and we are certainly working hard."
The first half was drab with very little goalmouth incidents. The best chances came early on.
In the fourth minute Calvin Andrew got clear on the left and fired across the face of the goal for Luton, but in the next minute a fine move at the other end saw Lee Peltier and Paul Warne combine to set up Lloyd Owusu, but the big striker failed to connect.
The second half started with Luton going close. From Darren Currie's left-wing corner, Jaroslaw Fojut seemed destined to score in a crowded goalmouth but the ball came back off the line.
Yeovil were now taking over and Ben Alnwick, in the Hatters goal, covered himself in glory with two magnificent saves.
In the 65th minute he stopped a stinger from Anthony Barry, always bright in Yeovil's midfield, and on 77 minutes he made an even better save when Peltier's shot looked to be heading for the bottom corner.
Kevin Blackwell, the Luton boss, sent out his assistant John Carver to face the media and he said: "It was a big improvement on our performance against Huddersfield on Saturday.
"With two home games to come, we hope this is a sign that we have turned the corner and can start climbing the table."