The first half got underway at the Estadi Nacional, with the hosts applying early pressure. Despite Inter's bright start, the Imps remained well organised throughout the opening 45 minutes, restricting the home side to a few clear-cut opportunities, all of which were comfortably dealt with by Jaylan Hankins.
The best chance of the half fell to Manuel Toledano in the 40th minute. After beating Javi Diaz to a loose ball, Toledano looked set to roll the ball into an empty net, only for Inter captain Alex Sanchez to produce a superb last-ditch block to deny him.
Juanma Pavon made an early change in the second half, introducing Yussef Flalhi in place of Facundo Alvarez, and the substitution proved to be inspired. Flalhi's pace and direct running immediately caused problems for the Inter defence and played a key role in the opening goal.
The breakthrough arrived in the 62nd minute. Flalhi latched onto a perfectly weighted through ball from Toledano, rounded the goalkeeper, and unselfishly squared the ball for Alex Mula to tap into an empty net, giving the Imps a 1-0 lead on the night.
Shortly afterwards, Juanma Pavon made a double substitution as Kike replaced Toni, while Graeme Torrilla made his welcome return from injury in place of Manuel Toledano.
Inter pulled a goal back in the 80th minute when Dacu capitalised on a defensive error before calmly slotting the ball past Hankins from inside the penalty area.
There was more positive news late on as Ethan Britto continued his return from a long-term injury that had kept him out since last August, while Gabri Cardozo was handed his debut as the Imps looked to see out the closing stages.
Kike had a golden opportunity to restore the lead moments later. Flalhi skipped past his marker before delivering a dangerous low cross into the area. Kike's first touch took him away from Alex Sanchez, but he was unable to keep his effort on target.
The final whistle confirmed a 1-1 draw on the night, but the Imps' commanding 3-1 first-leg victory in Gibraltar proved decisive, sealing a 4-2 aggregate triumph and booking their place in the second qualifying round of the UEFA Champions League.
Next up for the Imps is a meeting with Swedish champions Mjällby AIF, with the first leg taking place in Sweden next Tuesday before the return leg in Gibraltar.