Adam Le Fondre's penalty 13 minutes from time was enough to give the Royals their second league win of the season.
Referee Trevor Kettle pointed to the spot after he judged Luke Ayling to have brought down Le Fondre.
Yeovil went close when Byron Webster headed over, while Ed Upson forced a good save from keeper Alex McCarthy.
The visitors, looking for their first Championship win since their opening weekend win over Ipswich Town, struggled to create any clear-cut chances in a first-half dominated by Yeovil.
Royals boss Nigel Adkins then introduced Danny Williams and the midfielder volleyed former Real Madrid and Everton winger Royston Drenthe's deep cross wide of the post.
Yeovil were on top again after the interval, with on-loan striker Andy Williams coming inches away from breaking the deadlock after curling an effort narrowly wide.
But, after being fouled in the box on 76 minutes, Le Fondre recovered to slam his penalty past goalkeeper Wayne Hennessey for his third goal of the season.
Yeovil manager Gary Johnson was unhappy with Reading's late penalty:
"If the referee gives that as a penalty then he should have given one for us too.
"Our boys were magnificent today and they deserved more than they got. We outplayed a very good Reading team and our boys did everything but score.
"We kept creating chances and had lots of shots, and when they were on target the keeper made some good saves. I'm not sure you can do any more in a game and get beaten.
"We respect the opposition and think they are still one of the favourites to get promotion, so we're pleased that we competed more than adequately with them. I suppose that's why it's even more upsetting when it gets taken away from you by something out of your control.
Reading manager Nigel Adkins was pleased to see his side bounce back from their 6-0 defeat by Peterborough in the Capital One Cup:
"We're delighted with the three points and a clean sheet. You talk about performances all the time but we came away from home after a really challenging week with 2,000 supporters behind the goal and won, which is the important thing.
"After the week we've had, we asked whether we could go away from home again in what is our third away match in a week and win - and we did.
"The result and the performance midweek cast something over the club, but we've come away from home and done what we needed.
"Yeovil was always going to be a challenging fixture because we were expected to win."
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