The Premier League side found their feet early in the first half and it was only a matter of time before Wilfried Bony found the back of the net by the ninth minute.
The Swans had numerous efforts to improve their lead, but Kuban striker Djibril Cisse also had a number of chances to show that the home side could still pose a threat, despite conceding a goal before the half-time interval.
Michael Laudrup's men continued their dominance in the second half with plenty of possession, but after one fluffed attempt, Kuban managed to get the ball in the back of the net courtesy of Cisse.
The Frenchman fired the ball into Michel Vorm's net following some pressure from his side, but before the striker could begin celebrating, the linesman flagged him offside and the referee disallowed the goal.
Waves of attack came from the home side, but their threat was dampened following the sending-off of Xandao, who was dismissed by the match official in the 76th minute for a second bookable offence.
After going down to 10 men, the hosts continued to put pressure on their opponents, and their efforts paid off as they nabbed a late equaliser through Ibrahima Balde, who chipped the ball over Vorm, resulting in one point apiece.