ImagoDespite playing nearly the entire second half with 10 men following the Croatia midfielder's dismissal, Dortmnund's Patrick Owomoyela netted the second from close range in the 71st minute to give the champions their third league win in a row.
Dortmund have now pulled level on 16 points with Werder and Borussia Moenchengladbach with the trio three points behind leaders Bayern Munich who host Hertha Berlin on Saturday.
"It's a big disappointment," said Werder coach Thomas Schaaf. "We played too badly in the second half, we didn't have any confidence in our game".
Werder dominated the first half with Peru striker Claudio Pizarro seemingly unaffected by the transatlantic journey after playing away to Chile in a World Cup qualifier only 72 hours earlier.
But Dortmund went ahead three minutes before the break when Perisic confused his marker with a cheeky step over and rifled the ball into the roof of the net for his second Bundesliga goal since joining from Bruges in the close season.
The 22-year-old had already been booked for a wild lunge at Sokratis Papastathopoulos and a late tackle on the same player earned him a sending-off two minutes after the restart.
Lukas Schmitz hit the underside of the crossbar as Werder poured forward, only for the hosts to be undone at a corner.
The defence failed to clear properly and, as Mats Hummels hooked the ball back in, a poorly-executed offside trap left Owomoyela all alone to score from close range in his first league match of the season.
"We defended very well, we had a little bit of luck.... and I think we deserved it," said Dortmund coach Juergen Klopp.
