Bayern went into this encounter having scored 27 goals in its previous six Bundesliga matches, but it was frustrated until Sule's deflected effort beat the impressive Jiri Pavlenka.
Bremen's goalkeeper made a string of top saves prior to Sule's winner, while Thomas Muller squandered a great chance after Milos Veljkovic saw red in the 58th minute.
But, unfortunately for second-place Borussia Dortmund, which faces Freiburg on Monday (AEST), Bremen could not hold on, and Bayern is now four points clear in pole position with four games remaining.
Despite a bright Werder start, Bayern soon took control, and it would have been ahead if not for an excellent save by Pavlenka, who stuck out a leg to divert Serge Gnabry's close-range volley wide.
Gnabry was twice denied in quick succession shortly after the restart, Veljkovic on hand to clear a scuffed effort off the line before Pavlenka made a smart stop at his near post.
Pavlenka pulled off another superb save to deny Robert Lewandowski moments later, but Bremen's task was made even more difficult when Veljkovic received his marching orders after catching Lewandowski with an elbow.
Muller looked set to make Bremen pay for Veljkovic's petulance with 20 minutes remaining, only to head wide of a gaping goal.
Pavlenka was finally beaten five minutes later though, Sule's hopeful punt taking a wicked deflection off Davy Klaassen, while Lewandowski hit the crossbar as Bayern, which meets Bremen again in the DFB-Pokal on Thursday (AEDT), edged closer to a seventh successive title.