The Russians' progression to the knock-out stage was confirmed as Partizan Belgrade failed to beat Inter Milan later on the evening.
Neftchi offered precious little to suggest they are capable of overturning a six-point deficit in the remaining two games to qualify, an unlikely feat that is now mathematically impossible as Inter picked up a point in Belgrade.
Rubin's Alan Kasaev saw his shot blocked by Tarlan Guliyev in the seventh minute but Bebras Natcho went closer with the rebound, his shot just skimming the crossbar.
Natcho made amends in the 16th minute, though, picking out Dyadyun to nod the ball home following a short corner.
Neftchi struggled to find a way back into the game before the break and were lucky to keep the gap to a single goal as Jose Salomon Rondon pinged a header high and wide following Vitali Kaleshin's fine cross.
The Azerbaijani side almost found a way through following the restart, but Sergei Ryzhikov was equal to Bruno Bertucci's free-kick, tipping the ball round a post and to safety.
Rondon rattled the woodwork as Rubin launched a full-blooded assault on the hosts, Dyadyun then forcing a stunning fingertip save from Sasa Stamenkovic, who soon had to smother a drive from Gokdeniz Karadeniz.
All Boyukagha Hajiyev's men could do was push the visitors back into their own half and that tactic worked for most of the second half, with the eager Dyadyun restricted to shooting from distance.
Araz Abdullayev did wriggle past Rubin's high line to drill an effort at Sergei Ryzhikov 10 minutes from time, but his accuracy was sorely lacking.