By the time Bob Houghton, the English coach who took the southern Swedes to the 1979 final where they lost to Brian Clough's Nottingham Forest, received the warm applause of the crowd at halftime, Rosenberg had made his mark.
He stabbed home Pa Konate's pass in the 17th minute to give the Swedes a precious 1-0 lead which they held to claim all three points.
"This was our best victory in the Champions League, when you look at the opponent," Rosenberg told broadcaster Viasat after the final whistle.
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A small club like Malmo are unlikely to again reach the heights scaled by Houghton, who returned to the city for the first time in over 20 years to see a corner of the ground named in his honour.
They must content themselves with victories like the one orchestrated by Rosenberg.
His goals got them to the Champions League group stage last season and in their first home game he scored twice to give them victory over Olympiakos as they collected their only points.
"They (Shakhtar) were a lot better than Olympiakos," the 33-year-old said. "They're almost in the same class as Real and PSG.
"We had it tough after the goal, but in the second half I thought we were the better team."
Rosenberg could have doubled Malmo's tally with a second-half penalty but he let Nicolaj Djurdjic take it, only for the Serb to have his effort saved.
"He'll score the next one," Rosenberg said as the fans savoured another famous European night. "The most important thing is that we won today."
(Editing by Ed Osmond)
