Zenit striker Kerzhakov scored twice in a 4-0 friendly hammering of Azerbaijan at Arena Khimki to take his tally to 28 international goals.
The 31-year-old only needed one goal to surpass Beschastnykh's landmark of 26 and it took him only six minutes to find the back of the net, before he struck again 12 minutes in.
Kerzhakov played down his exploits and expressed his gratitude to former team-mate Beschastnykh for helping him to find his feet in the Russia squad when he was first called up.
"I am happy that I was able to set a new record, but the most important thing was to win," he said.
"As for goals, I'm always happy when I score. I would like to thank the previous record holder Vladimir Beschastnykh, who helped me to join the national team when I was just starting his way into it."
Kerzhakov hopes his side have heeded the lessons from a disappointing World Cup in Brazil, in which they failed to progress beyond the group stage, as Russia prepare for their Euro 2016 qualifying campaign.
He said: "I think that the players who were at the World Cup got an idea of what level of football at the highest level.
"They realised that in the games with the most serious contenders to play faster, save time, avoid unnecessary loss, and any, even the slightest mistake leads to big problems."
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