With the score level at 1-1 after the first leg, the visitors took control of the tie at the end of the opening 45 minutes when Nono's 25-yard strike was diverted into his own net by goalkeeper Sergei Ryzhikov.
The Spanish outfit continued their impressive display at the start of the second half and shortly after the hour, they doubled their advantage through Ruben Castro to put the tie out of the reach of their Russian opponents.
Read below to see how the action unfolded at the Tsentralnyi Stadion.
4.41pmRubin Kazan qualified for the knockout stages of this competition after a dominant performance in Group D. The Russian outfit won four of their six fixtures to finish ahead of Maribor, Zulte Waregem and Wigan Athletic, scoring 14 goals in the process.
4.44pmAs for Betis, they were forced to settle for a runners-up spot behind Lyon in Group I. The Spanish team, who used to be managed by West Bromwich Albion head coach Pepe Mel, scored just three times before Christmas, but a solid defence was enough to help them progress through to the last 32.
4.48pmBoth teams are used to featuring at the top end of the domestic tables, but neither have performed to their usual standards during disappointing campaigns in Russia and Spain. Kazan have the best defence in the Russian Premier League but nine draws sees them currently sit in 11th position. Betis have fared even worse in La Liga, winning just three times to sit in last place, 11 points from safety.
4.51pmWe are less than 10 minutes away from kickoff in Russia. This is probably a good opportunity to tell you that the winner of this tie will go on to face either Maribor or Sevilla in the last 16.
4.53pmWith the first leg ending 1-1 in Spain, Rubin's away goal means that Betis must score this evening to have a chance of progression. It took them just three minutes to score last week - they could do with a similar kind of start tonight.
4.58pmThe two teams are entering the stadium. It appears as though a decent crowd have turned out for what should be an extremely tight encounter.
1 minPremier League referee Michael Olivier gets the match underway. Apparently, the temperature is -8C - I would advise lots of running around!
2 minWhat an opportunity for Kazan! They broke forward in numbers after Betis gave possession away on the halfway line, but the ball across the box evaded everyone and Betis were able to clear.
5 minBetis have hardly had a touch of the ball in the opening stages, and Kazan appear to be in control. I can't imagine that the Betis players have experienced temperatures like this before.
8 minGood pressure from Kamil Mullin helps earn Rubin Kazan the first corner of the match, but tyhe delivery into the box fails to beat the first man and the Spanish outfit clear.
10 minCHANCE! Kazan should be ahead. Chris Mavinga was played in down the left-hand side and the Frenchman found Ruslan Mukhametshin with a precise cut-back to the edge of the box, but the midfielder could only volley over the crossbar.
13 minOut of nowhere, Betis created a three-on-two opportunity, but a pass was well cut out by the Ribin defence, with the ball ricocheting into the grateful hands of Sergei Ryzhikov.
16 minBetis have improved in the last five minutes, but their first opening on goal is blazed into the stands by Cedrick Mabwati.
20 minGabriel Calderon will be delighted with his side's response after their slow start in Russia. They are penning Rubin back in their own half, and the Spaniards now look the more likely to break the deadlock.
24 minBOOKING! Rubin attempt to ease the pressure by playing the ball across their own box, but they only get themselves into trouble, with Roman Sharonov going into the box for a foul on the edge of the area.
25 minWOODWORK! Betis strike the post! The free kick from the left caused confusion in the penalty area, but it eventually fell to Jordi Figueras, who turned before firing the ball against the post from eight yards.
29 minJordi Figueras is causing Rubin plenty of problems from set pieces, but on this occasion, his weak header goes straight at the goalkeeper.
32 minThe steam coming off the players' heads is quite a sight! Betis must be keen to get back to Spain!
35 minRubin haven't posed any kind of threat to the Betis goal since the opening 10 minutes, which is a surprise given Betis' abysmal form in La Liga. They will be happy to see the half-time whistle.
37 minCHANCE! That's shocking play from Kamil Mullin! The Betis backline misjudged a long ball and the Russian forward was clear down the left-hand side. However, rather than go direct towards goal, he stopped to wait for support and was dispossessed.
39 minThere's just five minutes remaining until half time, and the momentum has began to swing. The home side have started to press their opponents and it's beginning to have an effect.
41 minCHANCE! Now it's Betis' turn to make a strange choice when in a fantastic position. Cedrick Mabwati moved past the final defender, but despite having support to his right, he opted to shoot and his effort was blocked by Sergei Ryzhikov.
45 minGOAL! Rubin Kazan 0-1 Real Betis (Ryzhikov own goal)
45 minReal Betis move ahead in this tie thanks to a fortuitous effort from Nono. The midfielder fired the ball towards goal from 30 yards but with his effort going marginally wide, goalkeeper Sergei Ryzhikov has parried the ball back on target and into the net!
5.51pmMichael Olivier blows the half-time whistle, and Betis have edged into the lead in this second leg. It's probably deserved, but it was a cruel way for Rubin to fall behind, and they will be up against it in the second half. One more goal from Betis would leave Rubin requiring three.
5.55pmIt will be interesting to see how Rubin approach the second period. They started brightly enough and had their moments towards the end of the half, but they have looked open at the back and Betis could easily be further ahead. However, I can't see Rubin scoring three in 45 minutes, so they can't concede another goal if they want a realistic chance of making the last 16.
6.04pmThe two teams are slowly making their way back out in Russia. I imagine that there is a reluctance to go back out into such freezing conditions!
47 minLike in the first half, Rubin waste little time in breaking forward to put Betis on the back foot, but after earning an early corner, they can't produce a decent cross.
49 minBetis win a free kick 30 yards from goal, but Nono's effort on goal is more wayward than his shot in the first half and Rubin have a goal kick.
51 minThe Spanish side have come out for the second half focused on playing on the break, but after the lively Cedrick Mabwati advanced to the edge of the penalty area, his pass was over-hit, and the move came to an end. Bright stuff from Betis, though.
55 minA few stray passes are beginning to come from Kazan. Is the pressure getting to them? A last-ditch block from Roman Sharonov prevents a ball from Mabwati finding its target.
59 minCHANCE! Kamil Mullin breezes past three players before pulling the ball back to Gokdeniz Karadeniz on the edge of the penalty area, but just as it appeared that he only needed to hit the target to bring his side level, the ball deflected off a Betis defender to go out for a corner. That should have been a goal.
62 minRoman Eremenko, who netted a penalty in the first leg, decides to try his luck from 25 yards, but he can only drag his shot wide of the mark. It's getting a little desperate for the home side, but they are still well in this match.
64 minGOAL! Rubin Kazan 0-2 Real Betis (Ruben Castro)
64 minWhat a delightful goal from Ruben Castro! The striker was found by a delicate pass through the middle of the Rubin defence, and Castro proceeded to loft the ball over the advancing goalkeeper and into the net. Rubin need three goals in the final 26 minutes or they are bowing out of the competition.
68 minThis match could fall away from Rubin now. They have no choice but to leave men forward, but Betis look a strong threat in attack. It's almost an impossible task for Rubin to get back into this.
72 minThere's been a delay in play as both sides make alterations. In Betis's case, the changes will be more about protecting players for their league campaign and for the later stages of this competition.
74 minBetis will play the winner of the tie between Maribor and Sevilla. It's currently 2-2 on aggregate, but Sevilla hold the advantage on the away-goal rule.
78 minKamil Mullin gets clear to the right of the Betis defence, but his shot from the corner of the penalty area is straight at Antonio Adan. Just over 10 minutes remaining in Russia.
81 minSUBSTITUTION! Ruben Castro departs the action after giving his side a strong grip on his tie. It wasn't a stellar performance from the Spaniard, but his contribution has earned his side a place in the next round. Fernando Valera is his replacement.
84 minThe Betis players are queuing up to score a third in Russia, but Varela can't test Sergei Ryzhikov with a volley from the edge of the area.
88 minSevilla have taken the lead in Spain against Maribor, leaving their opponents requiring two goals to have a chance of progression. It's looking very much like an all-Spanish affair in the last 16.
90 minThere will be four minutes of added-on time. Is that really needed?
90+2 minIt's always a sign that your fans have given up on you when they start concentrating on mimicking the assistant referee! There's a group of around 50 Rubin supporters going back and forth with the linesman, jumping up and down in the process.
6.56pmThe final whistle goes in Russia, and Real Betis have advanced through to the last 16 of the Europa League with a comfortable win over Rubin Kazan.
6.58pmThe way that this match started, it was hard to see where the goals were going to come from for Real Betis, but they remained patient to deliver a composed display. It appears that they will meet Sevilla in the next round.
6.59pmThat will be all from Sports Mole for this match. Thank you for joining us, and we hope that you stick around for the remaining Europa League games that are taking place this evening. Goodbye for now.