However, in a repeat of the previous fixture at the Liberty Stadium, Kuban netted a last-minute equaliser through Ibrahima Balde to earn a share of the spoils.
Read below to see how the action unfolded at the Kuban Stadium.
4.31pmHello, and welcome to Sports Mole's coverage of the match between Kuban Krasnodar and Swansea City in the Europa League.
4.33pmAs the match between Swansea and Kuban entered injury time at the Liberty Stadium two weeks ago, it appeared as though this match wouldn't have too much riding on it. However, after Djibril Cisse netted from the penalty spot, this fixture has taken on much greater importance for Michael Laudrup's side.
4.36pmThe Swans are still sitting pretty at the top of Group A, but a defeat this evening could see their progress into the knockout stages placed in some doubt. A draw wouldn't be the end of the world, providing that Valencia beat St Gallen, but the Welsh outfit could do with collecting three points from their trip to Russia.
4.37pmThe team news is in from Russia. Fancy taking a look at it? I thought you might.
4.38pmSWANSEA CITY XI: Vorm; Tiendalli, Amat, Williams, Davies; Canas, De Guzman, Pozuelo, Dyer; Lamah, Bony
4.40pmKUBAN KRASNODAR XI: Belenov; Xandao, Dealbert, Kozlov, Melgarejo; Bugaev, Tlisov, Kabore, Popov; Khubulov, Cisse
4.41pmSWANSEA CITY SUBSTITUTES: Tremmel, Taylor, Rangel, Chico Flores, Britton, Routledge, Vazquez
4.42pmKUBAN KRASNODAR SUBSTITUTES: Baychora, Bucur, Zhavnerchik, Fidler, Ignatyev, Bueno, Balde
4.45pmAs you can see from Swansea's starting lineup, they have made seven changes to the team that lost at Cardiff City on Sunday. Star man Michu had already been ruled out through an ankle injury, but Laudrup has opted to make a further six alterations, including handing a rare start to Roland Lamah.
4.47pmAs expected, Djibril Cisse keeps his place in the Kuban team, while Swansea will need to keep an eye on midfielder Arsen Khubulov, who made an impression with his pace and power at the Liberty Stadium.
4.50pmPREDICTION! I don't mean to sound pessimistic Swansea fans, but after witnessing Kuban's quality two weeks ago, I think your side are going to find it tough going in Russia. Kuban to edge it 1-0 or 2-1.
4.54pmWe are just over five minutes away from kickoff at the Kuban Stadium I hope it's warmer than it is over here, but I very much doubt that it is!
4.57pmThe two teams are out on the pitch. We will be getting underway in just a couple of minutes.
0 minKuban get us started in Russia.
1 minHow is that not a yellow card? Xandao has jumped for the ball and handled it deliberately. Weird decision.
2 minSAVE! What a save! De Guzman whips the free kick in for Bony, who powers a header towards the bottom corner, but it excellently saved by Belenov.
4 minCHANCE! This match has started at 100mph. A through ball sends Cisse clear on goal, but even though Michel Vorm slipped before the Frenchman's shot, it went straight at the goalkeeper. And breathe...
8 minAfter nearly falling a goal behind, it has been all Kuban. They are playing the ball around much like Swansea do at the Liberty Stadium. Cisse looks a major threat in attack.
9 minGOAL! Kuban Krasnodar 0-1 Swansea City (Bony)
9 minWhat was I saying? Swansea take the lead through Wilfried Bony. Lamah danced his way past the right-back, before pulling the ball back towards the penalty spot. Two Swansea players appeared to get in each other's way, but Bony eventually fired the ball into the bottom corner from eight yards.
14 minThings have calmed down a bit in Russia now, but Swansea will be delighted with that opening goal. As I say that, Xandao heads straight at Vorm from a corner. Should have done better.
17 minThere are a ridiculous amount of horns and whistles going off in the stadium. It feels like South Africa in 2010 all over again. Swansea are still second best, despite the goal. They are struggled to retain possession in the final third of the pitch.
20 minCHANCE! I was just about to sing the praises of Roland Lamah, but he has just wasted a huge opportunity for his side. He got in behind the Kuban defence, but he dragged his shot wide of the far post with his weaker foot.
25 minKuban remain intent on looking for the ball in behind the Swansea defence, whether that be down the middle or down the flanks. They are having plenty of joy, apart from when they get caught offside. Swansea need to be careful.
27 minEFFORT! Before the game, I commented on Khubulov's pace and power, but he shows tremendous technique to get a volley away on the turn. It was straight at Vorm, but it was a fine effort.
28 minSAVE! I didn't expect much from this match before kickoff, but it was been a quality match so far. Swansea go up the other end, with Dyer testing Belenov with a left-foot curling effort from 25 yards.
32 minSwansea might be well advised to try to keep the score at 1-0 until the break. Kuban realistically need three points this evening, and the longer that the Premier League side can stay in the lead, more gaps should appear in the home team's defence.
35 minSloppy play from De Guzman lets in Ivelin Popov, but the Bulgarian slices his shot wide of the target. He should have at least tested Vorm.
39 minI can't overstate how entertaining this match has been. It's been end-to-end for 40 minutes, and it's surprising that we haven't had another goal. It could easily be 2-2 at the very least.
41 minEFFORT! When Dyer runs at the Kuban defence, they look terrified. The winger does so again, but his shot goes straight at Belenov from 20 yards.
45 minHALF TIME: Kuban Krasnodar 0-1 Swansea City
5.47pmWhat a fantastic first half, and it's been even better if you are a Swansea fan. The visitors are fortunate to have denied Kuban a goal, but the visitors are full value for their 1-0 lead. They just need to show more of a ruthless streak in front of goal.
5.51pmThere were as many as 16 shots in that opening 45 minutes, with both teams having eight apiece. However, Swansea have dominated possession, holding on to the ball for 66% of the play.
5.56pmThere is another English team currently in Russia for a Europa League tie. Wigan Athletic are playing Rubin kazan, but they are 1-0 behind at half time.
6.00pmThe two teams are heading back out onto the pitch.
46 minWe are back underway.
47 minSwansea are being pushed back at the start of the second half, and De Guzman saves the day for the visitors when Cisse attempted to get a shot away.
51 minSwansea threaten to break twice in the space of a few minutes, but the defence manage to clear the ball. The Premier League side look lively in attack, even without the likes of Michu, Shelvey and Routledge.
54 minCHANCE! What an unbelievable opportunity for Cisse! The ball is pulled back for the Frenchman, who is waiting on the edge of the six-yard box, but with the goal gaping, he missed his kick and Vorm claimed the ball. Should be 1-1.
56 minBOOKING! Dwight Tiendalli has been cautioned for barging a Kuban player in the back. He started to complain to the referee, before realising that the booking was fully deserved.
60 minIt's all Kuban as we move past the hour. Swansea need to get hold of the ball, or else they will inevitably concede. Their only outlet at the moment appears to be the pace of Dyer, but he is being well shackled off the ball.
62 minSUBSTITUTIONS! Double change for Swansea, who bring on Wayne Routledge and Angel Rangel for Roland Lamah and Nathan Dyer.
64 minThose alterations indicate that Laudrup is looking to shore up his defence, rather than showing much ambition to score a second. Rangel needs to help Tiendalli, because he is getting over-run on the right-hand side.
66 minSwansea work the ball well, before earning a corner on the left. The corner is curled in by De Guzman, but Williams's header goes several yards over the crossbar.
71 minSUBSTITUTION! Laudrup makes his final change of the night, and it's a bit of a shock to see Bony leaving the pitch for Alvaro Vasquez. The Spaniard has yet to score for Swansea.
73 minSHOT! Another chance for Kuban, and another chance for Cisse. The former Liverpool man shows superb strength to shake off two challenges, before dragging the ball wide of the far post.
75 minRED CARD! Well it appears that Xandao was cautioned for that handball in the first half, because he has just been red-carded after going through the back of Vasquez! It was his second yellow card, and it was fully deserved too.
79 minThis is a huge opportunity now for the visitors. I don't think it will change much in attack for Kuban, but there should definitely be more gaps at the back. Kuban have a free kick, but the ball goes out for a goal kick.
81 minDe Guzman looks to be struggling with a knock, but Swansea have already made their three substitutions.
85 minFantastic stuff from Swansea, but they can't add the final touches to a quite brilliant move. There must have been at least 25 passes before Routledge crossed to the back post for Vasquez, but the ball was just too high for the striker.
88 minThis is turning into a keep-ball session for Swansea. They have two minutes plus added-on time to hang on to what would be a superb result.
90 minThere will be four minutes of added-on time. Where has that come from?
90+2 minGOAL! Kuban Krasnodar 1-1 Swansea City (Balde)
90+2 minUnbelievable. Kuban have netted an unlikely equaliser, but unlike in the match at the Liberty Stadium, it was a well-worked goal. The ball was lofted over the Swansea defence to Ibrahima Balde, who lobbed Vorm from six yards.
90+4 minFULL TIME: Kuban Krasnodar 1-1 Swansea City
6.52pmSwansea have been left dejected by that equaliser. They had the game in the palm of their hand, but Balde's finish had denied them the opportunity to qualify for the knockout stages this evening.
6.53pmThat will be all from Sports Mole for this match, but please stick around - there are plenty of Europa League fixtures taking place this evening, and we have full coverage of many of them. Goodbye for now.