With two automatic qualification spots and one play-off place up for grabs in each group, Wales have rarely had a better chance of reaching a major tournament for the first time since 1958.
But Chris Coleman's side suffered an early scare after falling behind against an Andorra side looking to add to a meagre tally of five points from 82 qualifiers since being ratified as a FIFA nation in 2000.
Their hopes were thwarted by Bale, though, as the Real Madrid winger scored twice - his winning effort a curling a free-kick that came just nine minutes from time to spare Wales' blushes in the Group B clash.
Captain Ildefons Lima scored the hosts' first competitive goal in four years early in the first half by converting a penalty to give Andorra, ranked 199th in the world, hope of claiming only the second competitive victory in their history.
Bale soon levelled with a header and, just when it appeared that Andorra were going to hold on for a famous point, the 25-year-old produced a moment of quality that broke the underdogs' hearts and served as another example of why Real paid a world-record transfer fee for his services.
The visitors enjoyed the better of the opening exchanges but surprisingly fell behind in the sixth minute through Lima's spot-kick.
Wales immediately reassumed their dominance as they pressed to find a quick leveller, Bale offering a warning sign as to his threat in the air as he headed narrowly over the crossbar from Joe Allen's corner.
Andorra did not learn from that near-miss, though, and were punished by Bale after 22 minutes when he towered above the home defence to glance home Ben Davies' perfectly placed left-wing cross.
But Coleman's men were far from impressive going forward and only when Bale got into promising areas were they really able to trouble a surprisingly resolute Andorra defence.
The opportunities continued to come for former Tottenham star Bale, who saw a header acrobatically cleared off the line by midfielder Josep Ayala in a fitting demonstration of Andorra's heroic defensive effort.
Yet that effort proved to be for nought as Bale fired home from a set-piece at the second time asking after seeing his first effort saved by Pol, only for the referee to demand a retake due to encroachment in a costly error by Andorra striker Gabi Riera.
