Kieffer Moore scored for the second away game in succession to get Ryan Giggs' side off the mark inside 10 minutes and Harry Wilson — on target in Wales's previous away win 11 months ago — added a second before half-time.
Despite creating chances there were no further goals for the visitors, who are already guaranteed the cushion of at least a play-off place, regardless of where they finish in their qualifying group.
Wales is now unbeaten in five games since back-to-back away losses in June and are within a point of second-place Hungary, which it faces in its final qualifier on Wednesday (AEDT), while Slovakia is a point behind and has a game in hand.
Azerbaijan has just one point from its seven group matches and was behind early on through Moore's back-post header, the Wales striker leaping highest to meet Wilson's whipped corner.
Emil Balayev produced a good save to deny Moore a second goal but there was no keeping out Wilson, who headed home the rebound after Daniel James's curled shot from distance struck the crossbar and then the post.
Wales thought it had a third goal five minutes into the second half when Tom Lockyer headed in from close range, only for the referee to rule it out for Ethan Ampadu's shove on Balayev.
Wilson was next to be denied by Balayev with an angled drive just before the hour mark, while Moore was wayward with a couple of efforts as Wales was made to settle for two goals.