The 20-year-old reached the semi-finals for the first time in her career at the Nurnberger Gastein Ladies last week and maintained that momentum with a 6-0 6-4 win over Pavlyuchenkova.
Min, who had only been past the second round twice before her exploits in Austria, was full of confidence at the WTA International event in Bastad and dominated her opponent.
It took just 20 minutes for Min to secure an opening set in which a beleaguered Pavlyuchenkova won just seven points.
Things improved slightly for the Russian in the second set but Min was able to create eight break-point chances and only needed to convert 37 per cent of those to secure victory, with Pavlyuchenkova's13 double-faults contributing to her downfall.
Jana Cepelova ended a run of six successive first-round defeats as she also progressed on Monday with a 6-4 6-4 win over Rebecca Peterson.
The Slovakian won the opening four games of the match against the home favourite and, although Peterson fought back to 4-3, her attempts to take the set were in vain as Cepelova only conceded one point in her final two service games.
An error-strewn second set saw seven breaks of serve as neither player looked confident but the 21-year-old eventually found her rhythm to finish as she started with four successive games.
Chanelle Scheepers set up a possible second-round meeting with fourth seed Yaroslava Shvedova after she claimed a 6-3 6-4 victory over Colombia's Mariana Duque-Marino.
The final player progressing on the opening day of competition was Lara Arruabarrena after her opponent Irina-Camelia Begu retired midway through the second set with the Spaniard 6-1 4-2 ahead.