After a resounding 4-1 win away to promotion rival Schalke, Bremen made a blistering start as Niclas Fullkrug back-heeled a Mitchel Weiser cross past Thomas Dahne inside two minutes.
Kiel responded in kind, but Lewis Holtby's effort was ruled out for offside after a VAR (video assistant referee) review.
The next VAR check yielded a Werder penalty after Simon Lorenz was adjudged to have handled a Fullkrug header. Marvin Ducksch stepped up to make it 2-0.
Kiel was given a lifeline on the stroke of half-time. An Alexander Muhling corner caused pandemonium in the Bremen box, with Kwasi Wriedt's shot inadvertently going in off Fullkrug's outstretched leg.
Dahne had to dive full stretch to prevent Ducksch finding the mark with a brilliant free-kick soon after the restart. Fullkrug then sent a header wide, before Weiser went within a whisker of turning in a teasing cross into the six-yard box.
Kiel levelled against the run of play with 19 minutes remaining when Anthony Jung attempted to block off Wriedt, only to put Johannes van den Bergh's cross past his own goalkeeper.
After Fullkrug sent a header wide, Kiel completed an unlikely turnaround when substitute Ahmet Arslan's shot was saved, but Julian Korb buried the rebound in another huge twist in the promotion race, on a day Schalke won and St. Pauli drew.
Schalke is back on top after beating Sandhausen 2-1, but it took a stoppage-time winner from Simon Terrode to seal the deal before Sandhausen's Alou Kuol was sent off in the aftermath.
St Pauli is fourth on the table, and was frustrated in a 1-1 draw against Nurnburg, which equalised in the second minute of added time. The result meant St Pauli missed out on moving into third on the table to secure a play-off spot.