Milosevski - who won 59 caps for Macedonia and was in charge of football operations at the nation's football federation - tragically died in a car accident in March at the age of just 40.
Macedonia trailed Luxembourg 2-1 with 25 minutes to but Aleksandar Trajkovski's second goal - scored from the penalty spot - set up an exciting finish.
And Besart Abdurahimi proved the hero, netting a 92nd-minute winner for Macedonia in the Group C contest.
"I want to congratulate my players on the win," Gjurovski said.
"We dedicate this victory to the tragically deceased Petar Milosevski.
"The second-half substitutes changed the game - which was my intention - especially Besart Abdurahimi.
"We should be pleased with the way we got the three points, with courage and real determination.
"On Sunday against Ukraine, I have to say that we will play in the same way - offensively and as always, trying to do our best."
Luxembourg coach Luc Holtz acknowledged that the manner of his side's defeat made it a bitter pill to swallow.
Holtz said: "It is very hard to lose in this way... we were very unlucky at the end."
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