The defeat, their first in the league this season, cost them top spot to Porto who defeated Academica de Coimbra 3-1.
Sporting had won 11 and drawn two of their opening 13 matches this season and Jorge Jesus' side equalled a record set by Domingos Paciencia's 2011 team when they beat Moreirense 3-1 last weekend.
Madeira struck the only goal of the game when Danilo Dias headed past Rui Patricio at the far post.
"Uniao had one shot on goal," said coach Jesus, "and it wasn't even a shot, it was a header, while their goalkeeper saved three certain goals."
Goals from Danilo Pereira and Vincent Aboubakar, and Hector Herrera's stylish back-heeled effort, gave Julen Lopetegui's Porto a 3-0 lead before Rui Pedro replied late on for visiting Academica.
Benfica extended their unbeaten league run to seven games when they saw off Rio Ave 3-1 to remain third on 31 points, five off the pace.
Jonas' fourth-minute opener was cancelled out by Renan Bressan's superb long-range free kick for visiting Rio Ave nine minutes later.
Benfica's superiority eventually told when Jonas bagged his second goal in the 81st minute with a header and Raul Jimenez added a third.
Sixth-placed Rio Ave fell behind Vitoria de Setubal, who moved up to fifth with a 3-1 victory at bottom club Tondela, while Moreirense beat Nacional 2-0.
On Saturday, Arouca defeated Maritimo 4-1 and Vitoria de Guimaraes won 1-0 at Estoril.
(Writing by Ed Dove; Editing by Tony Jimenez)
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