But they could have been behind early on after a mix-up between debutant Ashley Williams and goalkeeper Lewis Price.
A lack of communication almost allowed Alphonse Leweck to profit from an under-hit back pass, before Williams managed to usher the ball to safety in an otherwise solid start.
It took Wales 15 minutes to settle and get their first chance which came from a corner but Carl Fletcher drove right-footed over the bar from 25 yards.
Lewin Nyatanga did have the ball in the net for Wales three minutes later from a Jason Koumas free-kick, only for it to be ruled out for offside.
Luxembourg tried to play passing football but never really looked like threatening and spent much of the first half defending.
The visitors were finding it difficult to put some fluency into their game and break down their hosts, but seven minutes before the break, they finally made the breakthrough.
Koumas found Eastwood on the right who controlled well, cut into the box and passed two players before firing right-footed into the bottom corner.
Eastwood almost pounced again when Luxembourg keeper Jonathan Joubert let a back-pass roll off his shin before he managed to scramble the ball clear.
He did though get his second three minutes after the restart.
Davies - winning his 50th cap - was somehow deemed to be onside down the right and he darted into the box before cutting back for Eastwood to score.
Manager John Toshack handed out debuts to Hull goalkeeper Boaz Myhill and Swansea's injury-plagued midfielder Owain Tudur Jones in the second half.
It has taken Jones two years to get this far after suffering 16 months of knee and ankle injuries since his first abortive call-up by Toshack.
As the game went on, the quality of football worsened with neither side really creating anything.
Substitute Cotterill did hit the post on 77 minutes from Davies' through-ball but chances were few and far between.
Luxembourg: Joubert, Lang (Peters 66), Kintziger, Hoffmann, Wagner, Leweck (Da Mota Alves 66), Strasser, Joachim (Kitenge 66), Remy, Mutsch, Oberweis. Subs Not Used: Bigard, Collette, Lucic, Ferreira, Scholer.
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