Rondon struck in the 99th minute for his fifth goal in the Europa League this season with substitute Dyadyun sealing victory with eight of the 30 extra minutes remaining after Levante had committed men to finding the equaliser which would have seen them through on away goals.
It had been a tight, tense tie which was played out in front of a sparse crowd that by the end of the night were shivering in the snow at the Luzhniki Stadium.
Bebras Natcho was involved from the off for Rubin with two long-range shots in the opening minutes.
Alan Kasaev sent a shot wide for the hosts and it took the visitors almost 20 minutes to have an effort on target, Papa Diop's 25-yard drive blocked and Garcia Ruben firing wide.
Jose Barkero and Christian Lell both fired over for the visitors with the former then curling an effort straight into the arms of Rubin goalkeeper Sergei Ryzhikov.
Gokdeniz Karadeniz lobbed the ball over for the hosts with Pablo Orbaiz's shot blocked by David Navarro on the stroke of half-time as the sides again failed to breach the opposition defence.
The game continued in much the same manner after the break as both sides looked for the winner with neither wanting to play for an extra 30 minutes ahead of their domestic duties at the weekend.
Navarro's header was comfortably gathered by the keeper while Natcho and Orbaiz fired wide and high.
Diop also put a shot over and although there was plenty of intent on both sides, neither had created a clear-cut chance.
It took until the 78th minute for either goalkeeper to be tested when Natcho's 25-yard shot was tipped over by Keylor Navas.
The Russians came within inches of what would have in all probability been the winner two minutes from time when Rondon's header was tipped round the post by Navas.
However, the 90-minute point was reached with the game goalless after 180 minutes with extra-time and possibly penalties looming.
There was little of note in the opening minutes before Rondon intervened to put the hosts ahead.
Natcho sent in a ball from the right which dissected the defence to find Rondon who got ahead of his marker and attacked the ball, sliding it home for his fifth goal in the Europa League this season.
Levante were showing far more urgency now and a venomous shot from distance by Sergio Ballesteros forced Ryzhikov to parry the ball over.
However, moments later and with men committed upfield, Levante conceded a second goal.
A giant throw by Ryzhikov found Dyadyun and he pounced on Diop's mistaken decision to allow the ball to bounce.
The Levante defender fell over and Dyadyun was away, keeping his composure as he slotted the ball home from outside the area.