Aziz Alijonov gave Neftchi the lead from the penalty spot after just eight minutes before Anvar Berdiev scored an all-important second 11 minutes from time on the counter-attack to seal the points for the Uzbeks.
Mahmoud Shelbaieh found the back of the net for Al Wehdat a minute into stoppage-time but the effort turned out to be little more than a consolation as Branko Smiljanic's team were unable to find a way past Hislatjon Chilmatov in the remaining six minutes of additional time.
"This was our first official game in both the AFC Cup and in Uzbekistan this year," said Sarkisyan.
"That's why we were happy to score such an early goal and then it was good that Berdiev scored a second but if you look at the whole game, Al Wehdat had the advantage.
"After the second goal we played defensively because our players were tired in the second half. But this victory has made us and our people very happy."