The world number 13 was facing compatriot Valeria Solovieva in the Azerbaijan capital and needed almost two and half hours to wrap up the match 7-5 6-4.
Pavlyuchenkova hit 16 double faults in the first set alone in extreme conditions which saw her call the trainer out for heat exhaustion after breaking to lead 3-1 in the final set.
As a reward for her victory, Pavlyuchenkova, who reached the quarter-finals of the French Open this year, will next play Elena Bovina.
Her 25 double faults is believed to be the highest number in a victory since Anna Kournikova had 31 in a three-set win at the 1999 Australian Open.
It is also believed to be the biggest number of double faults that a player has ever produced in a straight sets win on the WTA Tour.
The 25 points are the equivalent of six free games for Solovieva and was eight double faults more than Petra Kvitova hit during her entire victorious run at Wimbledon this year.
Pavlyuchenkova is seeded second at the hard court tournament in Baku behind Vera Zvonareva.