Former Chelsea winger Madueke unleashed a thunderbolt from distance to give the Gunners a deserved first-half lead and headed in from point-blank range at the start of the second half.
Martinelli then put the result beyond doubt, cutting in from the left and hitting a curling right-footed effort home from just outside the box.
Injury-hit Arsenal maintained their 100 percent record in the Champions League this season and have conceded just one goal so far.
The Gunners had already secured their place in the knockout phase before their trip to Belgium but now appear certain to secure a top-eight spot.
That would mean direct entry into the last 16, avoiding the need for a risky play-off.
Mikel Arteta’s Premier League leaders suffered their first defeat since August at the weekend, losing 2-1 at Aston Villa.
Ivan Leko, back at Brugge for a second spell as manager, was overseeing his first match after the Belgian club sacked Nicky Hayen on Monday.
Arteta, dealing with an injury crisis, made five changes to the side that lost to Villa, with Christian Norgaard starting at centre back and Viktor Gyokeres back in the starting line-up for the first time since November 1. (AFP)