The home team took advantage of Portugal's unfamiliarity with the Luzhniki Stadium's artificial turf as Kerzhakov broke clear on goal in the sixth minute following some quick one-touch passing featuring his Zenit St Petersburg team mates Viktor Faizulin and Roman Shirokov.
It was the striker's third goal in the first three qualifiers following a brace in last month's 4-0 drubbing of Israel.
The Real Madrid forward, who showed no ill effects from a shoulder injury he sustained in Sunday's Spanish league match against arch-rivals Barcelona, first tested Russia goalkeeper Igor Akinfeev with a low shot in the 11th minute.
"Today, I saw a Russian team that played with huge desire, huge commitment," Italian Capello, who replaced Dick Advocaat as coach following Russia's poor showing at Euro 2012, told reporters. "Nevertheless, it was a very tough match."
Capello's counterpart, Paolo Bento, blamed bad luck for his team's defeat.
"I don't think it was a fair result looking at the way the game was played," the Portugal coach said.
"In general we played a good match. We reacted well after the goal and we followed with our pre-game plan," he added.
"Russia played a great match but I know my team can play top quality football. We came here to win and are very upset now."
