Kukushkin got off to a good start when he broke Ferrer in the third game, but the Spaniard hit straight back to break him in the very next game.
Ferrer broke again in the eighth game, but this time it was Kukushin's turn to respond as he brought it back to 5-4 immediately. However, Ferrer won a mammoth 10th game, claiming the set point at the third time of asking.
The number four seed's serving was a lot more reliable in the second set as Kukushkin failed to break him at all, while Ferrer managed one break to take the set 6-3.
Kukushkin refused to roll over, however, and the unseeded Kazakh player broke his more-illustrious opponent twice in the third set to win it 6-4.
Ferrer was always the heavy favourite to win, though, and he booked his place in the next round by winning the fourth and final set 6-4, having broken his opponent three times and been broken twice himself.