Jose Gaya struck in the dying seconds as Spain avoided defeat in their opening Nations League fixture against Germany, leaving Stuttgart with a 1-1 draw.
But Gaya was able to volley into the net from close range five minutes into added-on time as the spoils were shared in both sides' first outing in almost 10 months.
West Ham forward Andriy Yarmolenko put the hosts ahead after a quarter of an hour and although Haris Seferovic levelled four minutes before half-time, Zinchenko settled matters midway through the second half.
Kieffer Moore struck 10 minutes from time – his third international goal in six games – as he latched on to Daniel James' inviting cross and rewarded Wales' superiority at the Olympic Stadium.
Kenny's first game in charge looked destined to end in a disappointing defeat until central defender Duffy headed home in stoppage time in Sofia to cancel out Bozhidar Kraev's 56th-minute opener at the Vasil Levski Stadium.
The striker opened the scoring from the spot just after half-time and while Vyacheslav Karavayev doubled Russia's lead, Aleksandar Mitrovic pulled one back. But Dzyuba book-ended the scoring to give Russia some breathing room.
Dominik Szoboszlai scored the only goal of the game 10 minutes from time to lift Hungary to a 1-0 victory in Turkey.
In Group D1, Brandur Hendriksson Olsen scored in the last minute as the Faroe Islands came from 2-1 down to claim a 3-2 victory over Malta.
The Faroes went ahead through Klaemint Olsen but goals either side of the interval from Jurgen Degabriele and Andrei Agius put Malta ahead, only for Andreas Olsen and Brandur Hendriksson Olsen to turn the game on its head.
Andorra claimed a point from a goalless draw against Lavia, who finished the match with 10 men following Vladislavs Gutkovskis' dismissal.