Nelson Ferreira fired Lucerne's opener after 16 minutes with Xavier Hochstrasser doubling the lead five minutes later.
Marco Streller reduced arrears in the 34th minute but Ferreira's second after 71 minutes made certain of the points.
The dismissal of Benjamin Huggel six minutes from time capped a miserable afternoon for Basle.
Lucerne move one point clear of FC Thun, who have a game in hand.
Innocent Emeghara scored a hat-trick as Grasshoppers edged out Servette in a seven-goal thriller.
The first goal arrived after five minutes for Grasshoppers defender Guillermo Vallori, but that was cancelled out in the 24th minute by Eudi Silva.
Emeghara twice restored the visitors' lead with goals after 29 and 52 minutes, with Servette levelling both times through Christopher Routis (49) and Stephane Nater (66).
But Emeghara's hat-trick strike from the penalty spot after 73 minutes proved to be decisive with Servette running out of ideas.
Neuchatel Xamax enjoyed their first win of the campaign, beating FC Zurich 2-0 thanks to late goals from substitutes Max Veloso (79) and Sebastian Wuthrich (90).