Belgian defender Peersman was given his marching orders 18 minutes from time for a challenge on Jens Toornstra at Stadion Feijenoord when the Eredivisie encounter was goalless.
Bottom of the table Dordrecht looked set to stop the rot by hanging on for a point, but Toornstra ended the visitors' resistance when he broke the deadlock four minutes from time.
Ruben Schaken then added insult to injury by making it 2-0 in stoppage time to heap more misery on Dordrecht, who have only five points from 13 games and face a battle to avoid an immediate return to the Eerste Divisie.
Ernie Brandts' side have now failed to score in their last four Eredivisie games, while Feyenoord have not conceded in four league matches and are up to third.
Luciano Slagveer went from hero to villain as Heerenveen suffered a 4-1 defeat at Ajax.
Slagveer scored his first goal of the season 18 minutes in to put Dwight Lodeweges' men in front, but was then sent off for a second bookable offence two minutes before half-time.
Ajax needed a Daley Sinkgraven own goal to draw level after 66 minutes, then two goals in the space of a minute from Anwar El Ghazi and Ricardo Kishna put the home side in command.
In-form Poland striker Arkadiusz Milik took his tally to five goals in his last four games for club and country with a penalty six minutes from time as Ajax moved just a point behind leaders PSV, who play Groningen on Sunday.
Aron Johannsson scored the only goal of the game to ensure AZ beat Vitesse to move up to fifth place, while Go Ahead Eagles ended a run of four games without a win in all competitions by beating NAC Breda 2-0.
Excelsior and Willem II drew 1-1 in Tilburg in the other game played on Saturday.
