Nuremberg's first blunder came when Thomas Paulus footed in a cross for a ninth-minute own-goal. In the 45th, goalkeeper Raphael Schaefer let Antonio da Silva's 40-meter free kick sail in the goal untouched.
"We scored their goals ourselves. You can't win like that," Nuremberg coach Wolfgang Wolf said. "Those are the kind of goals you get when you're bottom."
Also, Arminia Bielefeld beat Hannover 96 4-1 as a season high in goals was recorded for the two Sunday matches.
Benjamin Auer scored for Mainz in the 11th, helped when a defender fell trying to stop him, and Michael Thurk completed the team's scoring in the 52nd.
Stefan Kiessling volleyed in his fifth season goal in the 14th minute for Nuremberg, trying to cope with injuries to the likes of Marek Mintal, the Bundesliga's top scorer last season.
Nuremberg has yielded 13 goals in three matches and fell three points behind 17th-place Kaiserslautern. Mainz, just one point ahead to start the match, jumped four slots to 13th.
Bielefeld, once bottom itself, ran its unbeaten streak to five matches against Hannover. Michael Fink scored just 48 seconds into the game -- the fastest goal in the team's Bundesliga history.
Ghana's Isaac Boakye, a protege of former Bundesliga standout Anthony Yeboah, added goals in the 68th and 84th minutes.
Sporting was held to a 2-2 draw by Boavista, moving the Lisbon team into seventh place.
Sporting got its first goal from 19-year-old midfielder Nani Cunha in the 21st minute, and striker Liedson Muniz added another shortly after.
In the 46th, former Sporting player Joao Pinto headed in a goal for Boavista, and striker William Souza scored the equalizer in the 55th.
On Saturday, both FC Porto and Benfica drew. Porto was held to 0-0 by Setubal, while Benfica and Naval drew 1-1.
Auxerre dominated Paris Saint-Germain in the French first division, winning 2-0 on an own-goal from Edouard Cisse and a late header from Luigi Pieroni.
The hosts had several chances to increase their lead, including in the 12th minute when Benjani and Yann Lachuer collided into each other when chasing a loose ball in the penalty area.
Lachuer later created Auxerre's first goal in the 53rd minute when his curling free kick from the right hit the bottom of Cisse's foot and got past goalkeeper Lionel Letizi.
Four minutes from time, Pieroni headed in a corner to make it 2-0.
Feyenoord stayed close to the top of the standings after beating Willem II Tilburg 3-1.
Midfielder Jonathan De Guzman scored the first goal for Feyenoord in the eighth minute, and winger Romeo Castelen made it 2-0 in the 21st. Patrick Paauwe scored Feyenoord's final goal in the 55th, while Hans Denissen got one back for the hosts in injury time.
The win keeps Feyenoord in a tie for second place with AZ Alkmaar with 24 points, both one point behind leader PSV Eindhoven.
PSV beat FC Twente 1-0 on Saturday, while AZ topped ADO The Hague 2-0.
On Friday, Ajax was held to a 0-0 draw by SC Heerenveen, dropping the Amsterdam powerhouse to sixth place with 15 points.
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