The result lifted Schalke to 31 points, one off pacesetters Bayer Leverkusen, with Bremen, who had not lost since the first matchday back in August in all competitions, dropping to fourth on 28.
Bayern Munich, who earlier on Saturday crushed VfL Bochum 5-1, are third on 30 points after 16 matches.
Bremen and Schalke played a cautious first half with the hosts more aggressive and Schalke lurking for a counter attack.
Their patience paid off two minutes after the restart when Kuranyi broke the offside trap after a through ball from Lewis Holtby, sidestepped keeper Tim Wiese and slotted home for his eighth goal of the season.
The striker, desperate to win back a spot in the Germany squad ahead of next year's World Cup, turned provider in the 72nd minute when he set up substitute Jan Moravek, who had come on seconds earlier, to fire home Schalke's second goal, helped by a deflection.
DOMINANT BAYERN
Resurgent Bayern Munich demolished hosts VfL Bochum to record their third straight Bundesliga win.
Bayern, fielding the same team that crushed Juventus 4-1 in midweek to reach the Champions League knockout stage, broke Bochum's double defensive line in the 23rd minute when Olic floated a low cross for Gomez to sneak between two defenders and tap in.
The Bavarians, who have now won five in a row in all competitions, doubled their lead 11 minutes later when Bochum defender Mergim Mavraj deflected a seemingly harmless Danijel Pranjic cross into his own net.
Olic scored either side of halftime before unmarked Pranjic grabbed another with a shot inside the box in the 56th minute.
Bochum, in complete disarray since the first half, managed to score when Fuchs curled his free kick over keeper Hans-Joerg Butt in the 76th minute.
"It is difficult to stay in focus after such a win as our (Champions League) win over Juventus," said Bayern coach Louis van Gaal. "But my players did it. It is a bit of a shame not to have kept a clean sheet but after a 4-1 in Turin and a 5-1 in Bochum a coach can only be satisfied."
Hamburg thumped hosts Nuremberg 4-0 to stay close to the the top, in fifth place on 28 points.
Borussia Moenchengladbach were gifted three own goals from Hanover 96 players in a 5-3 win that consolidated their position in mid-table.
