The Swans were denied victory once again against Kuban Krasnodar as substitute Ibrahima Balde scored in added-on time to give the hosts a share of the spoils in Russia.
Wilfried Bony's ninth-minute goal - his eighth in 17 appearances since his club-record move last summer - looked to have been enough for the Swans, but Kuban - down to ten men following Xandao's 75th-minute dismissal - struck late on just like they had at the Liberty in the previous Group A fixture which ended in the same scoreline.
It proved a frustrating night in Krasnodar for Michael Laudrup's side, who had dominated this game with a performance that would have given the Great Dane plenty of positives as his team responded to the derby setback to Cardiff last weekend.
The Swans, who move to second in Group A, now have eight points from four games with Valencia on top with nine points following their 3-2 win in St Gallen.
Swiss side St Gallen are on three points, with the Swans needing two points from their remaining games at home to Valencia before the final group fixture in St Gallen.
The Swans made seven changes to the starting XI.
Three of the changes came in defence as Dwight Tiendalli and Ben Davies - fit again after a hamstring injury - started on the flanks while Jordi Amat came in to partner captain Ashley Williams.
Jose Canas got the nod in midfield while Alejandro Pozuelo took up the central attacking role behind Wilfried Bony.
Out wide, on-loan winger Roland Lamah made his second start of the campaign while Nathan Dyer offered the pace on the opposite side.
Garry Monk, Michu, Pablo Hernandez and Jonjo Shelvey were all unavailable and missed out on selection.
KUBAN: Aleksandr Belenov (capt), Xandao, Angel Dealbert, Artur Tilsov (Artem Fidler, 78), Djibril Cisse, Charles Kabore, Aleksei Kozlov (Ibrahima Balde, 74), Lorenzo Melgarejo, Roman Bugaev, Ivelin Popov, Arsen Khubulov (Vladislav Ignatyev, 66).
SUBS: Eduard Baychora, Gheorghe Bucur, Maksim Zhavnerchik, Gonzalo Bueno.
SWANS: Michel Vorm, Dwight Tiendalli, Jordi Amat, Ashley Williams (capt), Ben Davies, Jose Canas, Jonathan de Guzman, Alejandro Pozuelo, Nathan Dyer (Angel Rangel, 62), Roland Lamah (Wayne Routledge, 62), Wilfried Bony (Alvaro Vazquez, 71).
SUBS: Gerhard Tremmel, Neil Taylor, Chico Flores, Leon Britton.
The Swans made a rapid start at the Kuban Stadium, with Wilfried Bony denied by a superb save from home keeper Aleksandr Belenov after just 70 seconds.
Jonathan de Guzman's pinpoint free-kick found the striker 12 yards out, and his header - destined for the bottom corner - was tipped wide by the keeper at full stretch.
The drama continued and, in the fourth minute, a sublime volleyed pass from Artur Tilsov sent Djibril Cisse in on goal. The former Liverpool striker sprinted 50 yards goal but was denied by the legs of Michel Vorm.
And it wasn't long until the first goal arrived.
In the ninth minute, Jose Canas found Alejandro Pozuelo in space, and when the Spaniard raced into the box and touched left to Roland Lamah, the winger squared to Bony, who fired home from his second attempt.
The Swans continued to maintain their tempo, and a Pozuelo through ball almost sent Lamah in on goal only for the Belgian international to be thwarted by a last-gasp sliding challenge.
Kuban then went close themselves, Xandao heading straight at Vorm following a corner but it was the Swans who could - and should - have claimed the game's next goal.
When de Guzman threaded through a pass for the onrushing Lamah, the winger closed in on goal but his shot drifted just wide from an angle.
Both teams continued to probe, and Roman Bugaev tried his luck from 30 yards but Vorm comfortably watched it bounce past his near post.
Then Nathan Dyer went close to doubling the visitors' lead as he fired a left-footed shot following a one-two with Bony, but Belenov dived and again tipped the shot wide at full stretch.
The chances kept coming in this game, and next up was Ivelin Popov, but he could only fire over after being found in space in the Swans box.
Popov again tried his luck, capitalising on de Guzman's slip but the striker drove his effort into the advertising boards.
It was end-to-end stuff, and Dyer was denied by Belenov after he won possession 40 yards out before racing on and unleashing a dipping shot in the final action of the half.
HALF-TIME: Kuban Krasnodar 0 Swans 1
The home crowd were vocal and pushing their side on for an equaliser, and they created a decent chance in the 54th minute as Cisse got on the end of a cross just eight yards out, but he couldn't make a clean connection before the danger was cleared.
Cisse did have the ball in three net three minutes later as he latched onto a through ball, but it was disallowed for offside.
Laudrup made changes just past the hour mark and both came out wide as Angel Rangel replaced Dyer and Wayne Routledge came on for Lamah.
The Great Dane made his final change in the last 20 minutes as Alvaro Vazquez replaced scorer Bony.
But it was the opposing striker Cisse, who was in the thick of the action as he unleashed from an acute angle, but Vorm watched it drift wide of the far post.
Then, in the 75th minute, Kuban's hopes were given a blow as defender Xandao was shown a second yellow card after downing Vazquez.
From that point onwards it was about seeing out the victory.
But the hosts broke the hearts of the Swans with sub Ibrahima Balde striking late on in the four minutes of added on time as he beat Vorm to a loose ball to send the Kuban support into ecstasy.
It meant a point, not three, for the Swans, as they now look to confirm their place in the next round with games against Valencia and St Gallen to come.