After their shock loss to Northern Ireland, Fabio Capello's side needed to win to keep the pressure on Portugal in the battle for top spot in Group F.
They wasted little time as Kokorin struck inside 20 seconds and doubled his tally ten minutes before the break. Alexander Kerzhakov and Alexander Samedov joined him on the score-sheet, while Aurelien Joachim grabbed a Luxembourg consolation.
Russia had initially been frustrated by the weather as a heavy downpour forced officials to delay kick-off by an hour at the Central Stadium.
But once under way Kokorin struck, deftly clipping the ball over Jonathan Joubert from the impressive Kerzhakov's nod down.
Kokorin might have had a second soon after, but drilled wide from a Kerzhakov pass after a swift counter-attack.
Kerzhakov himself went close when Stefano Bensi cleared an effort off the line, but Kokorin eventually doubled the lead when he headed in from a Dmitry Kombarov free-kick.
Kokorin wanted a hat-trick before half-time but curled a speculative effort well over.
Sergey Ignashevich fired narrowly from the edge of the area, but Kerzhakov got the goal his performance deserved just before the hour when he flicked in from a corner. Kerzhakov looked for a second from a free-kick but failed to extend goalkeeper Joubert.