Calvin Andrew nodded in his fourth of the season in the 48th minute but the hosts could have won by a much greater margin, hitting the woodwork twice and being denied by visiting goalkeeper Steve Mildenhall time and again.
The win was the Hatters' fourth 1-0 home victory in succession and stretched their run of form to one defeat in 12.
Andrew set the tone for Luton's display with a 35-yard effort after just 80 seconds which had visiting goalkeeper Steve Mildenhall getting down low to gather.
The hosts moved the ball with purpose and, after Dave Edwards had a shot deflected wide in the 12th minute, the resulting Darren Currie corner saw Matthew Spring have a 14-yard header cleared off the line by Gary Dempsey.
Yeovil created an opening 60 seconds later when Zoltan Stieber played in Marcus Stewart, who could only fluff his effort straight at Dean Brill from just inside the penalty area.
However, that was the Glovers' only moment of joy in a one-sided first half that the Hatters dominated.
Drew Talbot should have opened the scoring in the 28th minute when he ran on to David Bell's pass, cut inside from the right-hand side of the six-yard box and crashed a left-footed effort against the underside of the crossbar and away.
Andrew had a powerful 16-yard volley blocked by Mildenhall in the 40th minute and, moments later, the Yeovil number one had to produce a fine double save to deny Edwards and then Currie as the ball fell loose.
The goal Luton's play deserved arrived three minutes into the second period as Bell whipped the ball in from the left and Andrew dived to head home from five yards.
The pressure continued as Mildenhall blocked with his legs from Currie in the 50th minute and Andrew then fired just past the post from 20 yards a minute later.
Talbot had a deflected shot cleared off the line by Matt Rose in the 72nd minute and Edwards then saw his glancing header from Currie's free-kick tipped on to the post by the impressive Mildenhall.
Yeovil were reduced to ten men in the 88th minute when Paul Warne received his second yellow card.