The 17-year-old Anderlecht striker opened the scoring after less than 90 seconds, taking full advantage of a goalkeeping blunder by Russia's Igor Akinfeyev.
Wednesday's game had been delayed after the Belgians had arrived in Voronezh only a few hours before kick-off after their plane was kept overnight in Moscow because of thick fog.
But the wait was worth it for the visitors when the normally reliable Akinfeyev gave the ball away near his own goal, allowing Lukaku a simple tap-in into an empty net to open his international account.
The highly-rated teenager doubled his tally midway through the second half after outmuscling two Russian defenders and beating Akinfeyev with a low shot into a far corner from 12 metres.
The Russians, urged on by a near capacity 30,000-strong home crowd in the industrial city some 530 kilometres south of Moscow, wasted numerous chances to hit back.
Despite the defeat, Russia coach Dick Advocaat was not too disappointed. "There are still some positives to take from this game," the Dutchman told a news conference.
"It was a good chance to test some young players. We were really unlucky, giving up the first goal right away, then we missed at least four great chances before they scored again."
The match was Russia's goodwill gesture to make amends with the Belgian Football Association for signing Advocaat.
The 63-year-old abruptly quit his post with Belgium's national team in April after just six months in charge before signing a four-year deal with Russia, replacing compatriot Guus Hiddink.
Advocaat's departure angered the Belgian FA, which threatened to take legal action against him before the two parties settled their case out of court.
