Patrik Schick equalised for Leverkusen after Omer Toprak had put Bremen ahead from a free-kick with only its second chance of the game.
Union Berlin climbed to fourth after a controversial 2-2 draw at home to Wolfsburg, which came from behind after Maximilian Arnold was sent off just after the break.
Renato Steffen gave Wolfsburg an early lead with a header, but Union striker Sheraldo Becker equalised with a crisp shot after squandering a clear chance.
It was 1-1 at the break, but Arnold was shown a straight red for a nudge on Liverpool loanee Taiwo Awoniyi just outside the area and Union midfielder Robert Andrich fired in the resulting free-kick on 52 minutes.
Union had the ball in the net again with an hour played, but the goal was disallowed as the referee judged Awoniyi had fouled Wolfsburg goalkeeper Koen Casteels.
Wolfsburg striker Wout Weghorst equalised on 67 minutes by converting a penalty after a handball by Union defender Marcus Ingvartsen.
Freiburg, meanwhile, set a new club record of five straight league wins, which has seen it climb from 14th to eighth in the table, with a 5-0 romp at home to Cologne, while Mainz now sits bottom of the pile after a 2-0 defeat to Eintracht Frankfurt.