Porto had a double chance at 0-0, but Inter goalkeeper Andre Onana denied both Zaidu Sanusi and Mehdi Taremi.
The second leg takes place at Porto’s Estadio do Dragao on Tuesday, 14 March.
Lukaku, who has played for Chelsea, West Brom, Everton and Manchester United, came on in the 58th minute for ex-Manchester City striker Edin Dzeko and became the match-winner after he reacted quickest when his header hit the woodwork.
Hakan Calhanoglu had also seen an earlier header pushed over, with Lautaro Martinez heading over when unmarked from six yards out.
Porto also had their moments when it was goalless, but Mateus Uribe and Taremi missed opportunities.
Otavio will now miss the second leg, but Porto will still fancy their chances of overturning the deficit at home in three weeks’ time.