Yeovil went ahead in the first half through a Shane Duffy header but they lost the plot in the second half when three players - Byron Webster, Joe Ralls and Kieffer Moore - were all sent off.
Webster went first, for conceding a penalty, but Adam Le Fondre missed the spot-kick. Goalkeeper Marek Stech saved it but was then credited with an own goal in the goalmouth scramble.
Ralls and Moore also saw red but Yeovil somehow held on for a point, with Stech making a series of fine saves near the end.
Reading's inconsistency has proved worrying as they aim to cement a place in the play-offs after winning five and losing three of their previous eight matches.
They had also lost their two previous home games, without scoring a goal. And yet in the two home games prior to that, they had scored 12 goals in wins over Bolton and Blackpool.
Yeovil, though bottom of the table at kick-off and three points off safety, had put together an unbeaten run of three matches. However, they had won only two of their past 15 away fixtures in all competitions.
Reading might have been overwhelming favourites but they were given an early warning sign when Yeovil midfielder Joe Edwards burst through only to shoot wide.
In response, Hal Robson-Kanu ran down the left flank and crossed low into the Yeovil area. Le Fondre looked handily placed to convert the chance but was denied by superb last-ditch tackle from centre-half Duffy, who is on loan from Everton.
Duffy again played a key role when Yeovil went ahead in the 20th minute. Luke Ayling slung over a free-kick from the right and, with Reading goalkeeper Alex McCarthy off his line and nowhere near to reaching the ball, Duffy easily headed into the empty net.
Yeovil could have increased their lead only for McCarthy to atone for his earlier error with flying save to keep out a fierce shot from Tom Lawrence.
Reading improved marginally before the interval but when Pavel Pogrebnyak thought he had equalised, after nodding in a Jordan Obita cross, the effort was swiftly disallowed for offside.
Deservedly jeered off by their fans at half-time, Reading upped the tempo in the second period. But Yeovil defended stubbornly during a barrage of six corners in the opening eight minutes of the half.
Ayling blocked a goalbound shot from Garath McCleary as did Kieffer Moore from Danny Williams. Pogrebnyak should also have done better than head an Obita cross straight at Yeovil keeper Stech.
The game exploded into life in the 66th minute, when Yeovil centre-back Webster was sent off for pulling back Reading substitute Royston Drenthe as he bore down on goal.
Le Fondre fluffed the resultant penalty, Stech saving well, but Reading equalised from the ensuing goalmouth scramble when Lawrence's attempted clearance went over the line off the back of the grounded Stech.
Two minutes later, Yeovil were reduced to nine men when midfielder Joe Ralls saw red for a scything challenge on McCleary. And then they were down to eight in the 88th minute when Moore went for a second bookable offence, a foul on Gunter, but they held on superbly for a draw.