Goals on either side of half-time by Swiss striker Eren Derdiyok and ex-Germany midfielder Simon Rolfes put Leverkusen in control in Bremen.
But the hosts hit back in the last 10 minutes as they poured forward only for Leverkusen's Stefan Kiessling to turn the ball into his own net on 83 minutes, just before Leverkusen were reduced to ten men.
Chile midfielder Arturo Vidal was shown a second yellow card, and after the subsequent red, on 87 minutes then Austria defender Sebastian Prödl scored the crucial equaliser in the 91st minute to complete the fight back.
"We fought for our luck, because we never gave up and we were rewarded," said Prödl. "After a game like that, a draw is okay. A victory wasn't deserved."
The draw leaves Leverkusen now 12 points behind run-away leaders Dortmund with defending champions Bayern in fourth.
The single point lifts Bremen out of the bottom three while Kaiserslautern, who were held to a 1-1 draw by Hamburg on Saturday, drop into the relegation zone.
Dortmund proved their status as Bundesliga winners-in-waiting with a 3-1 victory at Bayern's Allianz Arena on Saturday, their second win over Munich this season.
Bayern's director of sport Christian Nerlinger has said he now expects Borussia to win their first league title since 2002 with his team 16-points behind Dortmund.
"I think Dortmund will be champions, and rightly so," said Nerlinger. "We now have a different target, we have to go for second place now with everything we've got, and it won't be easy.
"It's a dangerous situation, which the players mustn't underestimate."
Goals by Germany defender Mats Hummels, Paraguay's Lucas Barrios and Turkey midfielder Nuri Sahin sealed Borussia's 18th win from 24 league matches, while Luiz Gustavo scored what proved to be Bayern's first-half consolation goal.
On Sunday, Stuttgart earned their 2-0 win at Eintracht Frankfurt despite losing French captain Matthieu Delpierre to a straight red card after only 15 minutes for pushing over Frankfurt's Maik Franz, who was also shown a yellow card in the incident.
But Stuttgart floored Frankfurt with two second-half goals in three minutes as Austrian striker Martin Harnik and Hungarian midfielder Tamas Hajnal scored for their second-from-bottom side.
After consecutive league defeats, this is an important win for Stuttgart coach Bruno Labbadia with his side still three points from safety in 17th with ten games left.
This is the seventh consecutive league game when Frankfurt have failed to score a single goal and the result leaves them 13th.
On Saturday, Hannover went third in the Bundesliga with a 1-0 win at Hamburg-side St Pauli.
This was Hannover's 14th win of the season from 24 matches and keeps them on course for a top-five finish and a place in Europe next season.
Nuremberg were denied their fifth straight win after Schalke's Raul netted his 14th goal of the season for the Royal Blues in Gelsenkirchen to seal a 1-1 draw.
Hoffenheim were beaten 2-1 by Mainz after Columbia midfielder Elkin Soto scored a late winner for the guests.
Germany striker Lukas Podolski netted an 88th-minute left-foot shot which sealed Cologne's 1-0 win over Freiburg and leaves his side now 11th in the table and five points from the bottom three. This was Cologne's fifth-straight win at home.
On Friday, two goals by Brazilian midfielder Diego helped Wolfsburg push themselves further from the Bundesliga's drop zone after a valuable 2-1 win over bottom side struggling Mönchengladbach on Friday.