Yeovil created the first chance of the game when Joseph Ralls attempted to crash home a volley from the edge of the area, hitting it sweetly but the ball was well-blocked.
Yeovil came close again soon after and should have taken the lead when Dan Seaborne rose to head towards goal, but he spurned the chance as the ball flew over the bar.
It then took a smart save by Reading goalkeeper Alex McCarthy to keep the scores level when Edward Upson let fly with a dipping strike from 25 yards.
Yeovil could have taken the lead moments later as good work from James Hayter saw the midfielder spin before firing just over the bar.
Reading might have taken the lead approaching the end of the half following a desperate scramble inside the Yeovil area, but Hennessey gathered well before Blackman could reach the ball six yards out from goal.
It should have been 1-0 to Reading again minutes later as Drenthe tricked his way past three Yeovil players before swinging a cross to the far post, where Williams marked a fantastic opportunity with a poor volley wide.
Reading took the lead in the second half when great play from Adam Le Fondre saw the striker rob the ball on the left wing, he then cut inside and was fouled in the six-yard box. The striker then stepped up to smash the ball straight down the middle, with Hennessey diving to his left.
The rest of the game played out with no real chances falling to either side, with Reading holding out during five minutes of added time to seal an important away victory.