The Welsh club had squandered a 2-0 lead from the first leg at Park Hall where Feronikeli scored twice late on to draw and set up a tense return in Pristina.
Scott Ruscoe's side withstood plenty of pressure from the Kosovan champions, but also looked a threat themselves, with Greg Draper denied in the first half before Ebbe headed in shortly after coming on.
New Saints will now progress to face Danish champions Copenhagen in the second qualifying round.
Kosovan champions Feronikeli, who had won through a preliminary round tie, started brightly at Pristina's Fadil Vokrri Stadium.
An early corner was headed wide before captain Lapidar Lladrovci saw his effort blocked and Besmir Bojku fired off target from 20 yards.
The visitors went close in the 26th minute when Aeron Edwards fed Draper, but the Feronikeli keeper was out quickly to make the save.
At the other end, midfielder Astrit Fazliu tried his luck from distance before, in first-half stoppage-time, Saints defender Keston Davies had to make an important tackle as the hosts again threatened on the break.
The Saints stepped things up following the restart, with an acrobatic effort from Jamie Mullan dropping wide.
The Welsh side finally broke the deadlock in the 67th minute when substitute Ebbe, who had just come on, headed in a cross from full-back Simon Spender.
Lladrovci put an effort wide following a corner, before the Saints then closed out some five minutes of added time to seal victory.