The hosts were on the front foot from the first whistle, with Keifer Moore sending a towering header just wide before Daniel James converted from Brennan Johnson’s cross to open the scoring.
That was no more than Rob Page’s side deserved, but Havakakan equalised with a bolt from the blue through Lucas Zelarayán’s clinical first-time finish on 19 minutes.
Armenia could barely believe their luck, and they soon found themselves ahead when Ranos, left criminally unmarked in the box, headed past Danny Ward after Aaron Ramsey had given the ball away cheaply.
That seemed to wake the Dragons up, who finished the half strongly, only for Joe Rodon, Johnson and Moore to be thwarted as they looked to level before the break.
Things continued in a similar fashion following the interval, with Rodon missing another headed chance and James fizzing wide. Wales were left regretting those missed chances when the visitors doubled their lead through a stunning Ranos strike, squeezing a fiercely struck low shot in at the near post from 20 yards.
Harry Wilson pulled one back, firing into the roof of the net after a long throw into the box caused havoc, but that was as close as they came to a comeback.
After Ranos had hit the woodwork, Zelarayán grabbed his second of the night to make it 4-2 and end Armenia’s nine-match winless run, while Wales, who had Moore sent off for a petulant off-the-ball kick-out at goalkeeper Ognjen Čančarević, missed out on the chance to go top of Group D in suffering their first home European Championship qualifying defeat since 2011.
Flashscore Man of the Match: Grant-Leon Ranos (Armenia)
