Reus fired in the opening and third goals, but Borussia should have won by more as Gabon striker Pierre-Emerick Aubameyang squandered three clear chances.
Right winger Henrikh Mkhitaryan capped a superb display with Dortmund’s second having provided the final pass for both of Reus’ goals.
After Bayern were held to a goalless draw at Eintracht Frankfurt on Friday, Dortmund took the chance to trim the Bavarian giants’ lead.
They have now scored 18 goals in their last four games and a staggering 64 in 20 games this season under new coach Thomas Tuchel.
Dortmund opened the scoring after nine minutes when Mkhitaryan fired in a cross, Aubameyang let the ball roll to Reus, who fired home at the far post.
Bremen levelled when Nigeria striker Anthony Ujah tapped home on 32 minutes after Matthias Ginter cleared off the line.
A superb cross off the offside of the boot from Mats Hummels found Mkhitaryan at the far post just before the break to head home on 44 minutes.
Reus added a third after Mkhitaryan’s final pass split the defence as the defeat left Bremen 14th in the table.
Borussia Moenchengladbach earned their sixth straight victory to go fourth with a 4-1 win at Hertha Berlin having been bottom in September with five defeats.
Gladbach blitzed Hertha with two goals in as many first-half minutes at Berlin’s Olympic Stadium from left-back Oscar Wendt, plus a solo effort from Brazil striker Raffael.
Gladbach grabbed a third when Swiss midfielder Granit Xhaka drilled home a penalty on 55 minutes after Ivory Coast winger Ibrahima Traore was fouled in the area.
Alexander Baumjohann converted a late penalty for Hertha after being fouled before Havard Nordtveit grabbed Gladbach’s fourth in added time.
The result boosts Gladbach ahead of Tuesday’s Champions League match at home to 2015 finalists Juventus while Hertha drop to sixth.
Gladbach are now just two points behind Schalke, who needed a late Leroy Sane equaliser in their 1-1 draw at home to Ingolstadt after the Bavarian visitors took a shock first-half lead.
Bochum-born Cameroon internationals Joel and Marvin Matip faced each other for the first time with Joel at centre-back for Schalke while Marvin captained Ingolstadt.
Huub Stevens picked up a point in his first game as coach of Hoffenheim in their goalless draw at Cologne.
Caretaker coach Stevens has been tasked with keeping second-from-bottom Hoffenheim in order for 28-year-old Julian Nagelsmann to make history next season as the Bundesliga’s youngest head coach.
Japan striker Yoshinori Muto claimed a hat-trick to rescue a dramatic point for mid-table Mainz in their 3-3 draw at bottom side Augsburg.
Having given Mainz a 2-0 lead before Augsburg roared back with three unanswered goals, Muto saved his best for last with a 93rd-minute strike. – Agence France-Presse