Slovakia continued to carve Luxembourg open at will and defender Peter Pekarik scored the hosts` third just before the break when he burst into the box and placed the ball past Jonathan Joubert.
Slovakia, who beat holders Spain in October, are on 15 points, three ahead of the European champions and six more than third-placed Ukraine.
David Alaba atoned for a penalty miss with a superb long-range second-half strike as Austria stayed on course for Euro 2016 with a comfortable 5-0 win away to Liechtenstein on Friday.
Martin Harnik and Marc Janko set the Group G leaders on their way with two goals in the first 16 minutes, quickly burying the hosts` hopes of repeating their shock 1-0 win over Moldova in their last match.
Alaba, Zlatko Junuzovic and Marko Arnautovic completed the win in the second half.
Mario Frick captained Liechtenstein at the 40 as he made his 118th appearance but never looked like adding to his record total of 16 goals.
Austria, whose only Euro finals appearance was in 2008 when they qualified automatically as co-hosts, remained unbeaten and top the group with 13 points from five games.
They took the lead after 14 minutes when Harnik ran on to a Junuzovic`s delightful flicked pass to fired past Peter Jehle and Janko tapped in Arnautovic`s low cross for the second two minutes later.
The visitors were awarded a penalty just after the half hour when Jehle fumbled the ball then clattered into Junuzovic as he tried to reclaim it, but Alaba spared the keeper`s blushes by sending a poor effort wide of the target.
The Bayern Munich midfielder made up for the miss when he collected a pass in midfield, side-stepped his marker and fired a dipping shot past Jehle from 25 metres just before the hour.
Marcel Sabitzer headed into the path of Junuzovic for the fourth in the 74th minute and Arnautovic rifled home the fifth in stoppage time to complete Austria`s fourth consecutive win in the group.
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