The single-match, neutral-venue tie, played at the Veltins-Arena in Germany, was rearranged after the scheduled fixtures in March were postponed due to the COVID-19 pandemic.
Yet Inter responded with Argentine striker Lautaro Martinez twice forcing good saves out of David Soria before Lukaku opened the scoring, latching on to a long ball, holding off Xabier Etxeita and shooting into the bottom corner.
Getafe responded well after the break with Jaime Mata seeing a header tipped over by Handanovic before they were given a great chance to get on level terms when the VAR spotted a handball in the box by Inter defender Diego Godin.
Yet 38-year-old substitute Jorge Molina put his poorly-struck penalty wide and from then on Inter never looked in danger.
After Lukaku, who has now scored in his last eight Europa League matches and has 30 goals in all competitions for Inter this season, missed a golden chance from close range, Inter made sure of the win through substitute Eriksen.
Moments after being introduced, the former Tottenham Hotspur midfielder, made no mistake as he took full advantage of a poor attempted clearance from Djene Dakonam.
Prior to the match, Inter CEO Giuseppe Marotta let it slip that the club had reached a deal to keep Alexis Sanchez at the club on a permanent basis with the official announcement to come on Thursday.