Russia, who went into the game level on points with Ireland and Slovakia, fell behind when Brazilian-born Marcos Pizzelli scored against the run of play in the 25th minute.
Pizzelli, who received Armenian citizenship in 2008, caught the Russian defence asleep and slid the ball into an open goal after going one-on-one with keeper Igor Akinfeyev.
Russia, held 0-0 by Armenia in Yerevan in March, equalised almost immediately with Pavlyuchenko's well taken volley.
The Tottenham Hotspur striker, who last month publicly criticised Russia coach Dick Advocaat for often selecting his favourite players, made it 2-1 just before the hour after a quick passing exchange between captain Andriy Arshavin and Igor Semshov on the left wing.
Pavlyuchenko, who was included in the starting line-up on Saturday after leading scorer Alexander Kerzhakov suffered a knee injury, sealed the points with a 73rd-minute penalty after Yuri Zhirkov was fouled by Sargis Hovsepyan.
"I think the last time I scored three goals in a match was when I played for Spartak," said Pavlyuchenko, who moved to England from Spartak Moscow in August 2008 and now has 19 goals in 40 international matches.
"Armenia is a good team but we were not expecting to fall behind. Luckily, we were able to recover quickly."
Advocaat was not totally satisfied though.
"Of course, I'm quite happy with the outcome but not how we had played," the Dutchman told a news conference.
"We had no margin for error in this match as we could not afford to lose any points. This made us look nervous."
The win lifted Russia up on to 13 points from six matches, with Slovakia hosting Andorra and Ireland playing away to Macedonia in later games. Armenia remain fourth on eight points.
