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.
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"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)
