Swansea's Europa League aspirations suffered a dent as Djibril Cisse's stoppage-time penalty saw Kuban Krasnodar deny them victory at the Liberty Stadium.
• Highlights: Swansea City 1-1 Kuban Krasnodar (US and Caribbean only)
Michu looked to have put the home side on course for a third straight Group A win when he grabbed his sixth goal of the season, and fourth of this European campaign, by sliding the ball beyond Aleksandr Belenov in the 68th minute.
But the visitors snatched a 1-1 draw and a valuable point when Swans keeper Gerhard Tremmel brought down substitute Ibrahima Balde, and former Liverpool forward Cisse calmly scored from the spot.
The result means Swansea remain top of Group A and move on to seven points, but this was a distinctly unimpressive display from the Welsh club against a limited opponent with just one win from their previous nine games.
Valencia's romp to a comprehensive victory over St Gallen in tonight's other group fixture moves the Spanish team onto six points, and Swansea have plenty of work to do to reach the last 32.
There had been few bright points during a tepid first half, but the hosts would have led had Jonjo Shelvey kept his composure.
Michu's first-time pass found the midfielder in acres of space, but his rushed shot was nowhere near finding the target.
Wilfried Bony volleyed over and Shelvey prodded wide from rare examples of incisive Swansea play, while at the other end Tremmel shovelled Maksim Zhavnerchik's drive wide and Dwight Tiendalli was fortunate to escape a red card after hauling down Lorenzo Melgarejo.
The hosts finally found some control after the break, with Michu making another telling intervention by racing onto a smart Alejandro Pozuelo pass to beat Belenov as he raced from his goal.
But they were pegged back in injury time after Tremmel brought down Balde having delaying his decision to come out to meet the striker, and Cisse made no mistake.
Swansea knew a win here would give them one foot in the knockout stages, but there was little sign of any urgency during a stuttering display.
Such was Swansea's lack of fluency, it took them 19 minutes to test Belenov, and then it was a tame effort from Nathan Dyer after a ricochet had helped the winger past two defenders.
A clearer chance followed seconds later as Bony and Michu combined to pick out Shelvey unmarked, but the midfielder snatched wildly at his shot which flew hopelessly wide.
Swansea were also experiencing a few scares of their own at the other end.
Chico Flores managed to steer a Arsen Khubulov pass over his own bar, just about, after a simple lofted ball from Charlos Kabore had found the hosts at sixes and sevens.
Tiendalli then had a lucky escape as, having realised his header back to Tremmel was short of power, pulled down Melgarejo, with the fact the incident occurred in a wide channel possibly saving the Dutchman from dismissal.
Another hopeful Kabore punt forward soon found the code to breach Swansea's defensive security again on the half-hour, but Popov dallied and then produced a clear dive under pressure from Neil Taylor as the chance was wasted.
Swansea simply had to improve after the break, but, aside from a rasping Shelvey effort which struck Igor Armas straight in the face when appearing to be bound for the top corner, the visitors were not unduly troubled.
However, as the half wore on Swansea gradually began to take a grip on proceedings, and Michu got the opener.
The Spain international and Pozuelo exchanged passes for the former to guide the ball home after racing into the box.
But Swansea could not kill the game and Shelvey's wayward pass allowed Kuban to launch their critical last-gasp attack.