But by making their run eight games without defeat, stretching back 14 months, Wales have now matched their nation's best-ever run.
Mike England's side went eight undefeated in 1981 but the real feather in the caps of Mark Hughes' men is that they have also equalled the eight games undefeated that the Welsh World Cup finalists of 1958 achieved before being beaten by Brazil in the quarter-finals in Sweden.
Wales have also never won their first three qualifying group games in any tournament in their history, and only twice before in 1985 and 1975 have they won three successive qualifying matches.
This was achieved with another display of dogged determination, guts and running and a perfect understanding of the team plan.
It was never pretty but the end result was another victory with Portugal edging just that little bit closer.
With fog sweeping in off the Caspian Sea and over the Tofig Bahramov Stadium here, named after the Azerbaijan-born linesman who allowed Geoff Hurst's World Cup Final goal in 1966, Wales were looking for some glory at last for their own nation.
With a squad stripped of seven star names - and then losing Danny Gabbidon after a late fitness test on his back problem - boss Hughes was forced to move skipper Speed back into a depleted midfield from his now familiar left-back spot for his country.
And that meant a recall in the heart of defence for Robert Page with Grimsby's Darren Barnard taking Speed's place for only his second start in 18 months.
Portsmouth's Carl Robinson also won his 10th cap in midfield, while Robert Earnshaw, the Cardiff youngster with 16 goals already for his club this season, played in Craig Bellamy's right-sided role.
It was the same tried and trusted shape to Hughes' side, with Hartson the loan striker supported by runners from midfield.
Surprisingly, Wales looked nervous at the start; Paul Jones sliced a clearance, then Page fouled Gurban Gurbanov and from the clever free-kick Samir Aliyev saw a shot just miss the far post.
It did not get much better as Simon Davies' sloppy pass conceded possession and the ball ended back in the Wales penalty area where Gurban Gurbanov saw a close-range effort touched around the post by a full stretch Jones. And all this in the first six minutes.
But from Wales' first genuine attack they caused havoc in the host's defence. Hartson brushed aside two players inside the box and set up Giggs 10 yards out but his close-range drive was superbly saved by Djahangir Hasanzadekh but he knew nothing about Giggs' follow up that cannoned off him and went for a corner.
But from the resulting set-piece delivered by Davies, Speed appeared unmarked beyond the far post to head Wales ahead, his first goal for his country since September 2000, and only his fifth in 71 internationals.
However, Wales did not look secure at the back and when Rashad Sadiqov fed Samir Aliyev, clear in the box, only a fine diving, point-blank block from Jones avoided an equaliser.
At the other end Giggs won a corner following a swaying, high speed run down the left and when Davies curled it in and Hasanzadekh made a mess of his punch, allowing Hartson to power a header against the crossbar and down onto the line.
Wales continued to exploit the width and another Davies corner on 37 minutes again found Speed arriving unmarked but this time Hasanzadekh pulled down the effort.
Early in the second half a sweeping move by Azerbaijan down the right produced a fine cross by Vadim Vasilyev which reached Mahmud Gurbanov in space but an outstanding tackle by Speed snuffed out the danger.
Substitute Fizulu Mamedov then fired in a swerving, low centre from the right, but Jones made an excellent plunging save, and Gurban Gurbanov sent in a low drive from the edge of the box that flashed wide.
Wales doggedly hung onto their lead with some solid displays from the lesser lights of Barnard and Delaney, with Carl Robinson scuffling and battling away in midfield.
Further chances were rare as they opted to defend in depth but one sweeping break saw Speed hook the ball on for Robinson, arriving at pace on the left, to volley over when he had time to control the ball.
But Wales did get their priceless second on 67 minutes when Davies curled in another free-kick and Hartson rose unchallenged to power a header into the net.
Late on a rare Barnard error on the left let in substitute Farukh Ismaylov, he raced at Jones from a tight angle, but saw his fierce shot saved superbly by the Southampton goalkeeper and victory was assured.
Azerbaijan Hasanzadekh, Neftaliyev, Kerimov (Fizuli Mamedov 46), Akhmedov (Asadov 75), Imamaliyev, Yadullaev, Makhmud Gurbanov (Farukh Ismaylov 61), Sadygov, Gurban Gurbanov, Vasilyev, Aliyev.
Subs Not Used: Magomedov, Ruslan Musayev, Gambarov, Azer Mamedov.
Booked: Sadygov, Farukh Ismaylov.
Wales Paul Jones, Delaney (Weston 71), Melville, Page, Barnard, Davies, Speed, Carl Robinson (Trollope 90), Giggs, Hartson, Earnshaw (Neil Roberts 90).
Subs Not Used: Crossley, Evans, Thomas, Williams.
Booked: Page, Barnard.
Goals: Speed 9, Hartson 68.
Ref: Luc Huyghe (Belgium).