Czech midfielder Plasil headed home from a Benoit Tremoulinas cross in the 24th minute and Bordeaux then relied on their sturdy defence to keep the visitors at bay.
Laurent Blanc's side, who have the league's best defence having conceded only 10 goals in 15 games, have 31 points and lead second-placed Montpellier, 2-1 winners at home to Le Mans earlier on Saturday, by four points.
PSG, who fired five past Boulogne earlier this week, remain ninth on 22 points.
Valenciennes moved up to third with a 3-1 home win against Monaco.
Lucho Gonzalez finally came to life to help Olympique Marseille snatch a 3-1 win at 10-man Nice.
Argentina midfielder Lucho, who has been criticised for lacklustre performances since joining from Porto during the close season, netted from close range for Marseille's second.
He also played a key role in a swift counter-attack that earned the visitors their first goal through Mamadou Niang on 19 minutes.
The Marseille defence, however, crumbled as so often this season and a Kafoumba Coulibaly volley put Nice level shortly after the half-hour.
The hosts played the second half with 10 men after Nigeria defender Onyekachi Apam was shown a straight red card for headbutting Argentina defender Gabriel Heinze.
Lucho got on the end of a Niang header to fire home from close range in the 77th minute with substitute Bakari Kone adding a third four minutes from time.
The win sent Marseille, who have a game in hand, up to seventh, six points behind Bordeaux.
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