The Royals won the game thanks to Danny Williams' third goal of the season in the 74th minute.
The first half of the match had failed to provide a goalscoring opportunity for either side but Reading deserved their win on the balance of the second-half action.
Royston Drenthe should have scored from a corner and Danny Guthrie's free-kick forced a fine save from Ben Hamer. The visitors' pressure then told as Guthrie's weighted pass found Williams who smashed the ball into the net from 12 yards.
Riga, whose side are just outside the relegation places, said: "We knew the difficulty of playing a team that didn't play three days ago as we had to do and certainly a team based on good organisation, good strikers and good counter-attacking.
"Before the game it was not an easy mission but we did it well - certainly for an hour. I think we had control of the game.They didn't create a lot of chances but then we didn't create a lot.
"We didn't really see the difference between a team busy with the play-offs and one busy with relegation so I'm sure the players have done what they have to do, but one mistake and you're punished."
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- Danny Guthrie