The former Newcastle striker fired the Russian side into a third-minute lead on a night when Michael O'Neill's home side were provided with plenty of evidence of the step up in class their progression has brought.
Rubin would have been 2-0 ahead at the break had it not been for goalkeeper Ryan Thompson's penalty save from striker Nelson Valdez, but the Jamaica international was beaten for a second time by Christian Noboa's piledriver five minutes after the restart.
The impressive Gokdeniz Karadeniz added a third in the 62nd minute after Ronan Finn's close-range header had been palmed away by Sergei Ryzhikov, who then saved Stephen O'Donnell's 64th-minute spot-kick to deny the League of Ireland side a consolation strike.
Rovers will renew their campaign with a glamour trip to Tottenham in a fortnight's time knowing the challenge will be no easier in north London.
The Hoops' very presence in the group stage of the competition - they are the first Irish club side to reach this stage - represents something of a fairytale, although the romance was quashed early on their big night.
Karadeniz, who was to prove a constant threat, made good ground down the left and cut inside before squaring the ball for Martins.
The Nigeria international span swiftly and although his left-footed shot was not the cleanest he has ever struck, his placement was more than adequate to send it into the bottom corner.
If that was exactly the start the Russians would have wanted in the unfamiliar surroundings of a packed Tallaght Stadium, it was just the reverse for the hosts.
To their credit, they gradually forced their way into the game. And although they were grateful to see Valdez fire over the top after Martins had once again caused problems on the edge of the box with nine minutes gone, they were not fazed by the task ahead of them.
They went close to an equaliser after 16 minutes when former Spurs midfielder Rohan Ricketts found space down the left and crossed for O'Donnell, whose extra-time penalty in Belgrade last month earned the club their passage to the group stage. He beat goalkeeper Ryzhikov to the ball, but headed over.
Rubin, however, continued to enjoy the larger share of the possession and really should have put the result beyond doubt nine minutes before the break.
Martins managed to get himself on the wrong side of central defender Craig Sives and drove into the box, where he was sent sprawling by the Scot in his efforts to make up lost ground.
Hungarian referee Zsolt Szabo immediately pointed to the spot and Valdez stepped up confidently.
However, Thompson dived to his right to keep out the spot-kick and made a second block before skipper Dan Murray hacked clear to spare the home side further damage and send them in at the break still in the game.
Martins did not re-appear after the break as his place was taken by Petr Bystrov, and it was the home side who started the brighter to pin the Russians back inside their own half.
But that was short-lived and the visitors extended their lead in style with five minutes of the second half gone.
Former Manchester United trainee could only clear Bystrov's deep cross to the edge of the penalty area, where Noboa did not need to break stride to rifle a stinging half-volley into the top corner despite Thompson's best efforts.
Rovers very nearly got themselves back into the game within seconds when Finn ran on to striker Gary Twigg's flick-on to head towards goal, but Ryzhikov made a fine reaction save to keep his effort out at point-blank range.
The Irish side's fading hopes were dealt a fatal blow on the hour when Karadeniz capped a fine individual display with an inch-perfect curling finish off the underside of the crossbar after latching on to Bebras Natcho's inviting pass.
O'Neill's men had a golden opportunity to grab a consolation goal four minutes later when Twigg was bundled to the ground inside the box by defender Cesar Navas.
But O'Donnell could not repeat his feat in Serbia as Ryzhikov saved with his legs as he dived to his left.
Rovers battled gamely as the clock ran down, but they were never able to find the quality they needed to take one of the half-chances which came their way as the visitors cruised towards the final whistle.