The Spartak Moscow midfielder finished a lovely move to score his 13th goal for his country one minute from time and earn Russia a deserved win.
The lively Artem Dzyuba went close after forcing a good save from Portugal goalkeeper Rui Patricio after 10 minutes and, from the resulting corner, the towering Zenit St. Petersburg forward's header crashed off the crossbar.
The hosts, playing in the southern city of Krasnodar, were dominant and captain Shirokov had another decent opportunity which Patricio saved at full stretch.
Debutant Goncalo Guedes had the best chance for the visitors in the first half, but Igor Akinfeev saved the 18-year-old's shot as the teams, who have both qualified for next year's European Championship, went into the break goalless.
Fernando Santos's side were without talisman Cristiano Ronaldo and they were on the back foot at the start of the second half as Pavel Mamaev went close with a shot from outside the penalty area.
Substitute Fedor Smolov thought he had put his country into the lead with 15 minutes to go, but he used his hand to direct the ball into the net from close range from a corner and was shown a yellow card.
Smolov broke free down the left with a minute left, his pass found Dzyuba and he gently laid the ball off to the onrushing Shirokov who slammed the ball past Patricio.
Slutskiy took as over as Russia coach from Fabio Capello in August.
(Reporting by Dmitriy Rogovitskiy, editing by Ed Osmond)
