The Imps made a bright start and looked the more dangerous side in the opening stages. Both Facundo Álvarez and Alex Mula had early opportunities but were unable to test Javi Díaz in the Inter goal.
The breakthrough arrived in the 16th minute when the referee pointed to the penalty spot after Manuel Toledano was brought down inside the area. Nano stepped up confidently and sent Díaz the wrong way, drilling his penalty into the bottom corner to give the Imps a deserved lead.
Ten minutes later, the lead was doubled. Nano's dangerous cross was only partially cleared, with the loose ball falling kindly to Toledano, who made no mistake from close range to score on his debut and put the Imps firmly in control.
The visitors pulled a goal back just before the interval. Maurizio Pochettino, son of current USA head coach Mauricio Pochettino, delivered a low cross into the box that, unfortunately, deflected off the outstretched leg of Christian Rutjens into the net, reducing the deficit before half-time.
Inter Club d'Escaldes began the second half strongly and applied sustained pressure, with Pochettino again at the heart of the danger as his effort from outside the area crashed against the crossbar.
The introduction of Yussef Flalhi and Kike just before the hour mark gave the Imps fresh attacking impetus, and they restored their two-goal advantage in the 66th minute.
Nano's corner found Bernardo Lopes at the back post, who intelligently vollied the ball back across goal to Christian Rutjens. His effort was blocked, but the rebound fell perfectly for Álvarez, who produced a clever backheel into the bottom corner to score on his debut and make it 3-1.
Rubén García, alongside fellow summer signings Ethan Jolley and Nico Pinto, was introduced during the closing stages as the Imps continued to control proceedings. García came agonisingly close to adding a fourth when his delicate dink beat the goalkeeper but struck the post before Erraji Jaouad cleared the ball off the line.
It was an impressive all-round performance from the Imps, who take a two-goal advantage into next Tuesday's second leg in Andorra, with a place in the second qualifying round firmly within their sights.